线性时变周期系统的能控性、稳定性分析与粗糙控制
|
摘要
线时变周期(LTVP)系统存在于许多实际工程技术领域,如弹性力系统、参数共振、质子加速器、天体力学、激光物理、卫星姿态控制、直升飞机传动系统、生态系统和经济系统中周期环境的竞争平衡等。线时变周期系统是一类重要而又研究成果较少的系统。粗糙集(Rough Set)理论是一种刻划不完整性、不确定性和不相容的数学工具,可以从数据本身中发现隐含的知识,解释潜在的规律。粗糙集理论为专家控制、智能控制提供了重要的理论基础。本文借鉴线性系统理论和现代鲁棒控制理论的思想,利用粗糙集理论方法,研究了LTVP系统能控性、能观性、渐近稳定性、Riccati稳定性分析问题,考虑了粗糙控制与网络控制问题,主要工作概括如下：
1.给出和改进了若干粗糙集数据处理的有效算法,提出对象编码后再扫描的方法,降低了复杂度,给出利用属性重要度进行属性约简、基于层次分析和简单相异矩阵属性约简、变精度粗糙集属性约简、区间数系统属性约简的算法。
2.利用MATLAB作为开发语言,编写了粗糙集数据处理方法的仿真工具箱软件程序,包括启发式属性约简,变精度属性约简,相异矩阵的属性约简,区间数属性约简,求上下近似,求核,规则生成等的程序,设计了图形用户界而。填补MATLAB软件粗糙集工具方面的空白。
3.给出了线性时变周期(LTVP)系统能控性的两个新的必要条件,该方法无须利用系统的状态转移矩阵,方便可行。讨论了时变广义系统的能控性,举例指出《IET, Control Theory and Application》上关于线性时变周期系统能控性的一个错误结论。利用对偶原理,所有能控性的结果都扩展到了能观性对应的结果。
4.解决了Riccati稳定的充分必要条件,此方法只依赖于系统本身的结构,不用依赖求解LMIs的可行解。得到了基于LMIs方法的LTVP系统Riccati稳定的充分条件,举例说明了线性定常系统系统的Riccati稳定在时延系统和鲁棒系统中的原因,设计了LTVP系统无记忆状态反馈控制器,鲁棒、H∞控制器,分析了LTVP时延系统稳定性。
5.综述和总结粗糙控制的各种应用,介绍粗糙集在过程控制的模糊隶属函数求取及倒立摆系统应用的方法,进行了LTVP网络控制系统稳定性分析与控制器设计,讨论了广义正定与稳定性的关系,指正广义正定方面的一个误解。
Linear time varying periodic (LTVP) systems can be found in many engineering technology field, such as flexible mechanics system, parameter resonator, proton ac-celerator, celestial mechanics, laser physics, satellite gesture control, helicopter drive system, ecosystem, economic system, period environment competition balance etc. Linear time varying periodic systems are a class of systems that are very important but have less research results. The rough set (RS) theory is a new mathematical tool to deal with imprecise, incomplete and inconsistent data. It can find hidden knowl-edge and explain latent rules from itself data. Rough set theory provides theory base for expert control and intelligence control. With the thought of linear system theory and modern robust control theory, and the method of rough set theory, the analy-sis of controllability, observability, asymptotic stability, Riccati stability and rough control, networked control of LTVP systems are considered. The main contents of the dissertation can be briefly described as follows:
1. The effective algorithms of rough set data analysis are presented and im-proved. The method of coding and scanning objects is considered. The algorithm complex degree is reduced. The heuristic attribute reduction algorithm with at-tribute importance, based on discriminative matrix attribute reduction algorithm, hierarchic analysis attribute reduction algorithm, variable precision attribute reduc-tion algorithm and interval number attribute reduction algorithm are presented.
2. By using MATLAB as the development language, the simulation tool box software of rough set data analysis is firstly programmed, including heueristic at-tribute reduction algorithm, disceraisility matrix attribute reduction algorithm, vari-able precision attribute reduction algorithm and interval number attribute reduction algorithm. The program of upper approximation, lover approximation realization equivalence relation, relatively attributes reduction, attribute core, etc. are ob-tained. The graphic user interface is designed. The deficiency of MATLAB software at rough set tool box aspect is filled up.
3. The new necessary conditions of controllability of LTVP systems are ob-tained. The method has feasibility and is more convenient. It dose not need cal-culating the state transition matrix. The controllability of time varying descriptor systems is discussed. An error conclusion of controllability of LTVP systems in the journal of IET control theory and application is pointed out by an example. By duality, all the obtained results can be extended the corresponding observability results.
4. The necessary and sufficient conditions of Riccati stability of linear time in-variant (LTI) systems are given. The method only depends on the system structure, without the calculation of LMIs feasibility. The necessary and sufficient conditions of Riccati stability of LTVP systems are provided. The applications of Riccati stability of LTI systems in time delay systems and robust control systems are demonstrated by two examples. The memoryless state feedback controller, robust controller and H∞controller of LTVP systems are designed. The stability of LTVP time delay systems is analyzed.
5. Survey and summary of rough control and networked control systems are provided. The method of rough control and selection of fuzzy member function are introduced. The control and simulation of networked control inverted pendulum are discussed. The stability of LTVP networked control systems is analyzed and the controller of LTVP networked control systems is designed. The relation between generalized positive definite and stability is discussed. A mistake on generalized positive definite application is pointed out.
1.给出和改进了若干粗糙集数据处理的有效算法,提出对象编码后再扫描的方法,降低了复杂度,给出利用属性重要度进行属性约简、基于层次分析和简单相异矩阵属性约简、变精度粗糙集属性约简、区间数系统属性约简的算法。
2.利用MATLAB作为开发语言,编写了粗糙集数据处理方法的仿真工具箱软件程序,包括启发式属性约简,变精度属性约简,相异矩阵的属性约简,区间数属性约简,求上下近似,求核,规则生成等的程序,设计了图形用户界而。填补MATLAB软件粗糙集工具方面的空白。
3.给出了线性时变周期(LTVP)系统能控性的两个新的必要条件,该方法无须利用系统的状态转移矩阵,方便可行。讨论了时变广义系统的能控性,举例指出《IET, Control Theory and Application》上关于线性时变周期系统能控性的一个错误结论。利用对偶原理,所有能控性的结果都扩展到了能观性对应的结果。
4.解决了Riccati稳定的充分必要条件,此方法只依赖于系统本身的结构,不用依赖求解LMIs的可行解。得到了基于LMIs方法的LTVP系统Riccati稳定的充分条件,举例说明了线性定常系统系统的Riccati稳定在时延系统和鲁棒系统中的原因,设计了LTVP系统无记忆状态反馈控制器,鲁棒、H∞控制器,分析了LTVP时延系统稳定性。
5.综述和总结粗糙控制的各种应用,介绍粗糙集在过程控制的模糊隶属函数求取及倒立摆系统应用的方法,进行了LTVP网络控制系统稳定性分析与控制器设计,讨论了广义正定与稳定性的关系,指正广义正定方面的一个误解。
Linear time varying periodic (LTVP) systems can be found in many engineering technology field, such as flexible mechanics system, parameter resonator, proton ac-celerator, celestial mechanics, laser physics, satellite gesture control, helicopter drive system, ecosystem, economic system, period environment competition balance etc. Linear time varying periodic systems are a class of systems that are very important but have less research results. The rough set (RS) theory is a new mathematical tool to deal with imprecise, incomplete and inconsistent data. It can find hidden knowl-edge and explain latent rules from itself data. Rough set theory provides theory base for expert control and intelligence control. With the thought of linear system theory and modern robust control theory, and the method of rough set theory, the analy-sis of controllability, observability, asymptotic stability, Riccati stability and rough control, networked control of LTVP systems are considered. The main contents of the dissertation can be briefly described as follows:
1. The effective algorithms of rough set data analysis are presented and im-proved. The method of coding and scanning objects is considered. The algorithm complex degree is reduced. The heuristic attribute reduction algorithm with at-tribute importance, based on discriminative matrix attribute reduction algorithm, hierarchic analysis attribute reduction algorithm, variable precision attribute reduc-tion algorithm and interval number attribute reduction algorithm are presented.
2. By using MATLAB as the development language, the simulation tool box software of rough set data analysis is firstly programmed, including heueristic at-tribute reduction algorithm, disceraisility matrix attribute reduction algorithm, vari-able precision attribute reduction algorithm and interval number attribute reduction algorithm. The program of upper approximation, lover approximation realization equivalence relation, relatively attributes reduction, attribute core, etc. are ob-tained. The graphic user interface is designed. The deficiency of MATLAB software at rough set tool box aspect is filled up.
3. The new necessary conditions of controllability of LTVP systems are ob-tained. The method has feasibility and is more convenient. It dose not need cal-culating the state transition matrix. The controllability of time varying descriptor systems is discussed. An error conclusion of controllability of LTVP systems in the journal of IET control theory and application is pointed out by an example. By duality, all the obtained results can be extended the corresponding observability results.
4. The necessary and sufficient conditions of Riccati stability of linear time in-variant (LTI) systems are given. The method only depends on the system structure, without the calculation of LMIs feasibility. The necessary and sufficient conditions of Riccati stability of LTVP systems are provided. The applications of Riccati stability of LTI systems in time delay systems and robust control systems are demonstrated by two examples. The memoryless state feedback controller, robust controller and H∞controller of LTVP systems are designed. The stability of LTVP time delay systems is analyzed.
5. Survey and summary of rough control and networked control systems are provided. The method of rough control and selection of fuzzy member function are introduced. The control and simulation of networked control inverted pendulum are discussed. The stability of LTVP networked control systems is analyzed and the controller of LTVP networked control systems is designed. The relation between generalized positive definite and stability is discussed. A mistake on generalized positive definite application is pointed out.
引文
1 Wiener N. Cybernetics:Or theControl and Communication in the Animal and the Machine[M]. Cambridge, MA, USA:MIT Press,1948.
2张庆灵,张雪峰,翟丁.控制理论基础[M].北京：高等教育出版社,2008.
3陈翰馥.控制理论的现状及对它的期望[J].信息与控制,1994,23(1)：34-37.
4 Zhang Q L, Liu W Q, David H. A Lyapunov approach to analysis of disctete singular systems [J]. Systems and Control Letters,2002,45:237-247.
5冯纯伯.自动控制学科的基础性研究课题[J].东南大学学报,1995,25(4)：22-29.
6 Dai L. Singular control systems[M]. Berlin:Spring-Verlag,1989.
7张庆灵.广义大系统的分散控制与鲁棒控制[M].西安：西北工业大学出版社,1997.
8熊军林,张庆灵.不确定广义系统的最优保成本控制[J].自动化学报,2004,30(4)：588-591.
9杨冬梅,张庆灵.广义系统[M].北京：科学出版社,2004.
10张庆灵,戴冠中,徐心和,等.离散广义系统稳定性分析与控制的Lyapunov方法[J].自动化学报,1998,24(5)：622-629.
11白玫.智能控制理论综述[J].华北水利水电学院学报,2002,23(1)：58-62.
12孙增圻.智能控制理论与技术[M].北京：清华大学出版社,1997.
13 Zadeh L A. Fuzzy set[J]. Information and Control,1965,8:338-358.
14郝丽娜,王伟,吴光宇,等.粗糙集-神经网络故障诊断方法研究[J].东北大学学报：自然科学版,2003,24(3)：252-255.
15 Malyaves V, Savkin A V. The problem of optimal robust Kalman state estimation via limited capacity digital communication channels [J]. Systems and Control Letters,2005,54:285-292.
16俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京：清华大学出版社,2002.
17王国军,陈松乔.自动控制理论发展综述[J].微型机与应用,2000,(6)：4-6.
18 Tom M M机器学习[M].北京：机械工业出版社,2003.
19 Pawlak Z. Rough sets[J]. International Journal of Information and Computer Science,1982, (11):341-356.
20韩祯祥,张琦,文福拴.粗糙集理论及其应用综述[J].控制理论与应用,1999,16(2)：153-157.
21 Yasdi. Rough sets learning and neural learning method to deal with uncertain and imprecise information [J]. Neurocomputing,1995,7(1):61-84.
22曾黄麟.粗集理论及其应用[M].重庆：重庆大学出版社,1998.
23 Golan R and Ziarko W. Methodology for stock market analysis utilizing rough set theory[J]. Proc. of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, New Jersey,1995,32-40.
24 Wong S K M, Ziarko W. On optimal decision rules in decision tables[J]. Bulletin of Polish Academy of Sciences,1985,33(12):694-696.
25 Lin T Y. Rough logic formalism for fuzzy logic controllers-a hard and soft com-puting approach[J]. Journal of Approximate Reasoning,1996,15(4):395-414.
26 Plonka L and Mrozek A. Rule based stabilization of the inverted pendulum [J]. Computational Intelligence,1995,11(2):348-356.
27 Peters J F, Ziaei K, Ramanna S. Approximate time rough control:concepts and application to satellite attitude control.Proc of RSCTC 98, warsaw, poland, 1998,491-498.
28谢克明,杨静.粗糙集理论及其在智能控制领域的应用前景[J].太原理大学学报,1999,30(4)：338-342.
29郭宇殊.粗糙控制中的数据预处理[J].矿业工程,2008,8(3)：64-67.
30郑光勇,叶为全,李斌,庄镇泉.基于粗糙集的过程控制规则挖掘算法及应用[J].微电子学与计算机,2006,23(6)：84-87.
31袁兵,江丽,朱宏辉.基于粗糙集理论的模糊控制规则的获取方法[J].武汉理工大学学报,2005,29(3)：453-455.
32邓九英,毛宗源,杜启亮,谭光兴.基于粗糙集的确定性控制规则决策模型[J].计算机工程,2008,34(10)：166-170.
33秦元勋,王慕秋,王联.运动稳定性理论与应用[M].北京：科学出版社,1981.
34 Yoshizawa T稳定性理论与周期解的存在性[M].郑祖庥译.南宁：广西人民出版社,1987.
35苏晓明,张庆灵.广义周期时变系统[M].北京：科学出版社,2006.
36 Sidi M J. Spacecraft dynamics and control[M]. Cambridge:Cambridge University Press,1997.
37章仁为.卫星轨道姿态动力学与控制[M].北京航空航天大学出版社,1998.
38张庆灵,杨冬梅.不确定广义系统的分析与综合[M].沈阳：东北大学出版社,2003.
39王战平,赵春.一类周期种群系统的稳定性分析及最优控制问题[J].生物数学学报,2008,23(2)：225-230.
40施文武,严洪森,汪峥.一种多周期随机需求生产/库存控制方法[J].控制与决策,2007,22(9)：994-999.
41王林泽,赵文礼.用闭环反馈周期脉冲抑制分叉和混沌运动[J].控制理论与应用,2006,23(3)：487-490.
42 Sreedhar J, Dooren P V. Periodic descriptor system:solvability and condition-ability[J]. IEEE Transactions on Automatic Control,1999,44(2):310-313.
43 Yan W Y. Decentralized control techniques in periodically time-varying discrete-time control systems[J]. IEEE Transaction on Automatic Control,1992,37(10): 1644-1648.
44 Vicente H, Ana U. Pole-assignment problem for discrete-time linear periodic systems [J]. International Journal of Control,1987,46(2):687-697.
45 Bose T, Chen M Q, Joo K S, Xu G F. Stability of two-dimensional discrete sys-tems with periodic coefficients [J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications. II:Analog Dig. Signal Process,1998, 45(7):839-847.
46 Bittanti S, Colaneri P, Guardabassi G. H-controllability and observability of linear periodic systems [J]. SIAM J.Control Optim,22(6):889-893.
47张棣,赵晓强,高占海.空间周期解的理论与应用[J].南京大学学报(数学半年刊),1987,21(1)：37-49.
48王慕秋,王联,吕绍明.关于大系统周期解的存在性[J].科学通报,1987,(13)：972-975.
49陈文成.动力系统的近周期性[J].中国科学(A辑),1995,25(4)：344-348.
50梁家荣,商立群,商立军.时变广义线性系统周期解的存在性[J].2000,30(6)：
51梁家荣,刘永清.广义系统的周期解[J].控制理论与应用,1997,14(4)：595-598.
52 Bamieh B, Pearson J, Francis B, Tannenbaum A. A lifting technique for linear periodic systems[J]. Systems & Control Letters,1991,17(2):79-88.
53 Yamamoto Y. New approach to sampled-data control systems-a function space method[C]. Proceedings of the 29th conference on decision and control, Honolulu, HW 1990,1882-1887.
54 Hu L S, Cao Y, Shao H. Constrained robust sampled-data control for nonlinear uncertain systems[J]. International Journal of Robust and Nonlinear Control, 2002,12(5):447-464.
55汤玉东,邹云.线性离散周期奇异系统的可解性与渐进稳定性[J].控制理论与应用,2004,21(4)：614-616.
56 Yame J J, Hanus R. On stabilization and spectrum assignment in periodically time-varying continuous-time systems [J]. IEEE Transactions on Automatic Con-trol,2001,46:979-983.
57 Kabamba P T. Monodromy eigenvalue assignment in linear periodic aystems[J]. IEEE Transactions on Automatic Control,1986,31(10):950-952.
58王平,李铁寿,吴宏鑫.线性周期系统特征值指数的配置[J].自动化学报,2004,30(4)：530-538.
59陈叔平.关于周期线性系统的能控性和能稳定性[J].高校应用数学学报,1990,1(5)：111-114.
60 Hewer, G. A. Periodicity, detectability and the matrix Riccati equation, SIAM [J]. Control Optim,1975,13(5):1235-1251.
61 Guo G, Qiao J F, Han C Z. Controllability of periodic systems:continuous and discrete[J]. IEE proc.Control Theory Appl,151(4):488-490.
62 Colaneri P, Kucera V. The model matching problem for periodic discrete-time systems[J]. IEEE Transactions on Automatic Control,1997,42(10):1472-1476.
63 Joseph B, Jamel F, Harry H, et al.Stability of fast periodic systems with time lags[J]. IEEE Transactions on Automatic Control,1989,34(4):462-465.
64陈阳舟.周期时变线性系统的一般线性二次型最优控制[J].控制理论与应用.2002,19(4)：415-418.
65 Liu H P, Daniel W C, Ho, Sun F C. A constructive approach to approximate linear periodic systems[J]. IEEE Transactions on Automatic Control,2007,52(3): 541-546.
66谈侃,王朝珠.线性时变周期系统的鲁棒稳定及比控制[J].自动化学报,1996,22(5)：611-614.
67翁爱治.二维周期系统的指数型一致渐进稳定[J].福州大学学报,2004,32(1)：6-34.
68陈喆,王宏禹,邱天爽.适用于LPTV系统的周期自适应滤波器的研究[J].电子与信息学报,2003,25(7)：884-891.
69 Campell S L, Terrel W J. Observability for linear time-varying descriptor system. SIAM Matrix Analysis[J]. Application,1991,12(4):484-496.
70 Bassam A, Bamieh J, Pearson B. A general framework for linear periodic sys-tems with applications to H∞ sampled-data control[J]. IEEE Transactions on Automatic Control,1992,37(4):418-435.
71 S. Lall and G. Dullerud. An LMI solution to the robust synthesis problem for multi-rate sampled-data systems[J].Automatica.2001,37:1909-1922.
72 Brunovsky P. Controllability and linear closed-loop controls in linear periodic systems[J]. Differ. Equ.1969,6(2):296-313.
73 Farhood M, Beck C L, Dullerud G E. Model reduction of periodic systems:A lifting approach[J]. Automatica,2005,41:1085-1090.
74 Gad E, Nakhla M. Efficient model reduction of linear periodically time-varying systems via compressed transient system function [J]. IEEE Transactions on Cir-cuits and Systems-Ⅰ:Fundamental Theory and Applications. I:Reg. Papers,2005, 52(6):1188-1204.
75 Duverrdier A, Lacaze B. On the use of periodic clock changes to implement linear periodic time-varying filters[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications. Ⅱ:Analog Dig. Signal Process,2000, 47(11):1152-11159.
76 Zhang P, Ding S X, Wang G Z, Zhou D H. Fault detection of linear discrete-time periodic systems[J]. IEEE Transactions on Automatic Control,2005,50(2): 239-244.
77 de Souza C E, Trofino A. An LMI approach to stabilization of linear discrete-time periodic systems[J]. International Journal of Control,2000,73(8):696-703.
78 Wei Y Y, Robert R B. Control of linear discrete-time perodic systems:a de-centralized control approach[J]. IEEE Transactions on Automatic Control,1992, 37(10):1644-1648.
79 Rezai M, Ito M R, Lawrence P D. Modeling and simulation of hybrid control systems by global Petri nets [A]. Proceedings of the 1995 IEEE International Symposium on Circuits and Systems [C]. Piscataway, NJ, USA:IEEE,1995: 908-911.
80岳东,彭晨,HanQL网络控制系统的分析与综合[M].北京：科学出版社,2007.
81 Zhang L Q, Shi Y, Chen T W, et al. A new method for stabilization of networked control systems with random delays [J], IEEE Transactions on Automatic Con-trol,2005,50(8):1177-1181.
82 Walsh G C, Ye H, Bushnell L G. Stability analysis ofnetworked control systems [A]. Proceedings of the 1999 American Control Conference [C]. Piscataway, NJ, USA:IEEE,1999:28762880.
83于之训,蒋平,陈辉堂.具有传输延迟的网络控制系统中状态观测器的设计[J].信息与控制,2000,29(2)：125-130.
84顾洪军.网络控制系统建模及性能分析方法的研究[D].北京：清华大学,2001.
85戴冠中,郑应平.网络化系统及其建模,分析,控制与优化[J].自动化学报,2002,28(增刊)：60-65.
86 Halevi Y, Ray A. Integrated communication and control systems:Part Ⅰ-analysis [J]. Journal ofDynamic Systems, Measurement and Contro,1988,110(4):367-373.
87 Murray R M, Astrom K J, Boyd S P, etal. Future directions in control in an information-rich world [J]. IEEE Control Systems Magazine,2003,23(2):20-33.
88 HALEVIY Y, RAY A. Integrated communication and control systems:part I-analysis[J]. Journal of Dynamic System Measure Control,1998,110(4):367-373.
89 Nilsson J B. Bernhardsson B. Wittenmark. Stochastic Analysis and Control of Real-time Systems with Random Time Delays. Automatica,1998,34(1):57-64.
90 TarnT J, Xi N. Planning and control of internet-based teleoperation [J]. Tele-manipulator and Telepresence Technologies V,1998:189-193.
91 Walsh G C, Ye H. Scheduling of networked control systems[J]. IEEE Control Systems Magazine, vol.21,2001:57-65.
92范明哲,于海斌,周悦.并行计算在网络化控制中的机遇与挑战[J].信息与控制,2003,32(2)：97-101+107.
93 Mei Yu, Guangming Xie, Long Wang. Stabilization of Networked Control Sys-tems with Transmission Delays[J]. IEEE International Conference on Systems, Man and Cybernetics.2004,1764-1769.
94 Wei Feng, Ji-Feng Zhang. Mean square stabilization control of switched systems with stochastic disturbances[C], The 43rd IEEE Conference on Decision and Control,2004.
95 Nilsson J. Real-time Control Systems with Delays[D]. Ph. D. dissertation. Swe-den:Lund Institute of Technology,1998.
96于之训,陈辉堂,王月娟.时延网络控制系统均方指数稳定的研究[J].控制与决策,2000,15(3)：278-281,289.
97 Zhang W, Branicky M S, Phillips S M. stability of Networked Control Systems [J]. IEEE Control Systems Magazine,2001,21 (1):84-99.
98谢林柏,方华京,王华.网络化控制系统的信息调度与稳定性研究[J].控制与决策,2004,19(5)：589-591.
99黎善斌,王智,张卫东,等.网络控制系统的研究现状与展望[J].信息与控制,2003,32(3)：239-244.
100 Nilsson J, Bernhardsson B, W ittenmark B. Stochastic analysis and control of real-time systems with random time delays [J]. Automatica,1998,34(1):57-64.
101 Hespanha J P, Naghshtabrizi P, Xu Y G. A survey of recent results in networked control systems [J]. Proceedings of the IEEE,2007,95(1):138-162.
102 Montestruque L A, Antsaklis P. Stability of model-based networked control sys-temswith time-varying transmission times [J]. IEEE Transactions on Automatic Control,2004,49(9):1562-1572.
103龙承念,代双凤,关新平.网络控制系统的补偿策略[J].吉林大学学报(信息科学版),2004,22(4)：438-443.
104王智,王天然,Song Y Q,等.工业实时通讯网络(现场总线)的基础理论研究与现状(上)[J].信息与控制,2002,31(2)：146152,163.
105 Tipsuwan Y, Chow M Y. Controlmethodologies in networked control systems [J]. ControlEngineering Practice,2003,11(10):1099-1111.
106 Lincoln B, Bernhardsson B. Optimal control over networks with long random delays [A]. Proceedings of the InternationalSymposium on Mathematical Theory of Networks and Systems [C]. France:University of Perpignan,2000:1-7.
107 Lin H, Zhai G, Fang L, etal. Stability and H∞performance preserving schedul-ing policy fornetworked control systems [A]. Proceedings of the 16th IFAC World Congress on Automatic Control [C]. Prague, Czech:ElsevierScience,2005.
108 Nilsson J. Real-time ControlSystemswith Delays [D]. Sweden:Lund Institute ofTechnology,1998.
109 N. B. Almutairi. Adaptive Fuzzy Modulation for Networked PI Control Systems. Ph. D. dissertation,2002.
110 Huo Z H, Fang H J. Fault-tolerant control research for networked control system under communication constraints [J]. Acta Automatica Sinica,2006,32(5):659-666.
111朱其新,胡寿松.网络控制系统的能控性和能观性[J].控制与决策,2004,19(2)：157-161.
112 Feng W, Zhang J F. Mean square stabilization controlof switched systemswith stochastic disturbances [A]. Proceedingsof the 43rd IEEE Conference on Decision and Control [C]. Piscataway, NJ, USA:IEEE,2004:3714-3719.
113 Slowinski R. Intelligent decision support-handbook of applications andad-vances of the rough sets theory[M]. Dordrecht:Kluwer Academic Publishers, 1992.
114张文修,吴伟志.粗糙集理论介绍和研究综述[J].模糊系统与数学,2000,14(4)：1-12.
115 Wygralak M. Rough sets and fuzzy sets-some remarks on interrelations[J]. Fuzzy Sets and Systems,1989,29(3):241-240.
116 Nanda S et al. Fuzzy rough sets[J]. Fuzzy Sets and Systems,1992,45(2):157-160.
117 Banerjee M and Pal S K.Roughness of a fuzzy set. Information Sciences,1996, 93(3,4):235-241.
118 Skowton A et al. From rough set theory to evidence theory. Advances in the Dempster Shafer Theory of Evidence[J]. New York:John Wiley and Sons Inc. 1994,193-236.
119 Nejman D. A rough set based method of handwritten numerals classification[M]. Institute of Computer Science Reports, Warsaw University of Technology, War-saw,1994.
120 TeghemJ et al. Use of rough sets method to draw premonitory factors for earthquakes by emphasizing gas geochemistry. In:Intelligent Decision Support-Handbook of applications and Advances of the Rough Sets Theory [J]. Dordrecht: Kluwer Academic Publishers,1992,165-179.
121 Deja R. Conflict model with negotiations.In:Institute of Computer Science Re-ports[M]. Warsaw University of Technlolgy, Warsaw,1995.
122 Hu Xiaohua et al. Mining knowledge rules from databases-a rough set ap-proach[J]. Proc. of IEEE International Conference on Data Engineering, Los Alamitos,1996,96-105.
123 Tsumoto S et al. Extraction of domain knowledge from databases based on rough set theory[J]. IEEE International Conference on Fuzzy Systems, New Jer-sey,1996,748-754.
124 Tsumoto S et al. Automated discovery of Medical expert system rules from clinical databases based on rough sets [J]. Proc. of Second International Conf. on Knowledge Discovery and Data Mining, USA,1996,63-72.
125 Jelonek J et al. Rough set reduction of attributes and their domains for neural networks [J]. Computational Intelligence,1995,11(2):339-347.
126 Peng C et al. Multivalued neural network and the knowledge acquisition method by the rough sets for ambiguous recognition problem[J]. Proc. of the IEEE Inter-national Conference on Systems, Man and Cybernetics, Beijing,1996,736-740.
127 Yasdi R. Combining rough sets learning and neural Iearning2method to deal with uncertain and imprecise information[J]. Neurocomputing,1995,7(1):61-84.
128 Slowinski R. Rough set approach to decision analysis[J]. AI Expert, March 1995, 19-25.
129 Slowinski R et al. Rough set sorting of firms according to bankruptcy risk[J]. In:Applying Multiple Criteria aid for Decision to Environment Management, Dordrecht:Kluwer Academic Publishers,1994,339-357.
130 Slowinski R et al. Rough set reasoning about uncertain data[J]. Fundamenta Informaticae,1996,27(2,3):229-243.
131 Parsons S et al. A rough set approach to reasoning under uncertainty[J]. Journal of Exprimental and Theoretical AI,1995,7(2):175-193.
132 Ruhe G and Gesselschaft F. Rough set based data analysis in goal2oriented soft-ware measurement[J]. Proc.of IEEE International software Metrics Symposium, Los Alamitos,1996,10-19.
133 Wojcik Z et al. Application of rough sets for edge enhancing image filters [J]. Proc. of IEEE International Conference on Image Processing, Los Alamitos, 1994,525-529.
134 Jackson A et al.Rough sets applied to materials data[J]. Acta Materialia,1996, 44(11):4475-4484.
135 Collette T and Szladow A.Use rough sets and spectral data for building pre-dictive models of reaction rate constants[J]. Applied Spectroscopy,1994,48(11): 1379-1386.
136 Aijun A et al.Discovering rules for water demand prediction-an enhanced rough set approach[J]. Engineering Applications of Artificial Intelligence,1996,9(6): 645-653.
137 Wojcik Z et al.Structural modeling using rough sets[J]. Proc.of IEEE Interna-tional Conference on Fuzzy Systems, New Jersey,1996,761-766.
138 Nurmi H et al. Probabilistic,fuzzy and rough concepts in social choice[J].European Journal of Operational Research,1996,95(2):264-277.
139 Lambert Torres G et al.Data Mining into a Control Center Database via Rough Set Techniques [J]. Proc.of the International Conference on Intelligent Systems Applications to Power Systems(ISAP'97), Seoul,1997,246-250.
140张琦,韩祯祥,文福拴.一种基于粗糙集方法的电力系统故障诊断／警报处理的新方法[J].中国电力,1998,31(4)：32-38.
141王珏,苗夺谦,周育键.关于Rough Set理论与应用的综述[J].模式识别与人工智能,1996,9(4)：337-344.
142庾慧英,刘文奇.变精度粗糙集模型中取值范围的确定[J].昆明理工大学学报(理工版),2005,20(6),109-111.
143张雪峰,石凡等,粗糙集数据分析系统的程序实现[J].辽宁石油化工大学学报,200424(3)：66-70.
144 Saaty T L. A scaling method for priorities in hierarchical structures[J]. Journal of Mathematical Psychology,1977,15(3):234-238.
145张雪峰,张庆灵.粗糙集数据分析系统MATLAB仿真工具箱设计[J].东北大学学报：自然科学版,2007,28(1)：40-43.
146赵晨,诸静.过程控制中的一种数据挖掘算法[J].武汉大学学报(工学版),2005,38(5)：131-134.
147宋申民,陈兴林,段广仁.基于粗糙集理论与进化计算的时滞系统Smith控制[J].系统仿真学报,2006,18(8)：2247-2249.
148张倩生.基于粗-模糊神经网络的决策控制[J].控制理论与应用,2005,22(2)：330-334.
149李炜,谢刚,谢克明.一种改进型的粗糙-神经网络PID控制器设计[J].太原理工大学学报,2004,35(3)：251-253.
150赛英,陈伟.从不一致例子中挖掘规则的粗集方法MIE-RS[J]计算机工程与应用,2000,10：22-23.
151赵卫东,盛昭瀚.基于粗集理论的一种归纳学习[J].方法管理工程学报,2000,14(4)：38-42.
152 Nakamura A. A rough logic based on incomplete information and its application [J]. International Journal of Approximate Reasoning,1996,15:367-378.
153 Marzena Kryszkiewicz. Rough set approach to incomplete information sys-tems[J]. Information science,112,1998, pp:39-49.
154 Shan N. An incremental learning algorithm for constructing decision rules [M]. Technical CS-93-02,Dept. of Comp. Sci. Univ. of Regina, Canada,1993.
155 Shan N,Ziarko W. Data—based acquisition and incremental modification of classification rules[J]. Computational Intelligence,1995,11:357-370.
156 Tong Lingyun, An Liping. Incremental learning of decision rules based on rough set theory [J]. Intelligent control and automation,2002, Proc. of the 4th world congress on intelligent control and automation,2002, Shanghai, China, pp:420-425.
157 J. W. Grzymala—Busse. LERS:a system for learning from examples based on rough sets. In:Slowinski, R. (ed.):Intelligent decision support [J]. Handbook of applications and advances of rough sets theory. Kluwer Academic Publishers, Boston,1992, pp:3-18.
158 Sienkiewicz J. Rough set and rough function approaches to the control algorithm reconstruction[M]. Institute of Computer Science Reports, Warsaw University of Technology, Warsaw,1996.
159 Mrozek A et al. Methodology of rough controller synthesis[J]. Proc. of IEEE International Conference on Fuzzy Systems, New Jersey,1996,1135-1139.
160 Czogala E et al. Idea of a rough fuzzy controller and its application to the stabilization of a pendulumcar system[J]. Fuzzy Sets and systems,1995,72(1): 261-273.
161 Arima M et al. Fuzzy logic and rough sets controller for HVAC systems[J]. Proc. of IEEE WESCANEX Communications, Power, and Computing, New York, 1995,133-138.
162张雪峰,宋文安.具有周期T的线性时变系统的稳定性[J].全国青年管理科学与系统科学论文集,1991,1(1)：534-538.
163仝茂达.线性系统理论和设计[M].合肥：中国科学技术大学出版社,2004.
164唐万生,李光泉.广义系统的能控,能观性判别条件[J].自动化学报,1995,21(1):63-66.
165 Petersen I R. A stabilization algorithm for a class of uncertain linear sys-tems [J]. Systems & Control Letters,1987,8:351-357.
166 Petersen I R, McFarlane D C. Optimal guaranteed cost control and filtering for uncertain linear systems [J]. IEEE Transactions on Automatic Control,1994, 39(9):1971-1977.
167 Campbell S L. Singular systems of differentials equations[M]. pitman advanced publishing program, Sanfrancisco London Melbourne,1980.
168 H. M. AI-Ramani, G. F. Franklin. Linear Periodic systems:Eigenvalue assign-ment using discrete periodic feedback[J]. IEEE Tras.Automat. Contr.1989,34: 99-103.
169 S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory[M]. SIAM Studies in Applied Mathematics. SIAM, Philadelphia, Pennsylvania,1994.
170 R. Datko.Solutions of the operator equation A* K+KA+KRK=-W. In: Semigroups of Operators:Theory and Applications. A. V. Balakrishnan, Ed. Birkhauser,2000.
171 Vincent D. Blondel, Alexandre Megretski. Unsolved Problems in Mathematical Systems and Control Theory[M]. New Jersey, USA:Princeton University,2004.
172 G. R. Duan, G. W. Irwin, G. P. Liu. Roubust Stabilization of Descriptor Linear Systems via Proportional-plus-derivative State Feedback.Proceedings of Ameri-can Control Conference San Diego, Califormia.1999,6:1304-1308.
173 Wohnam W M. Linear Multivariable Control:A Geometric Approach,3rd edn[M]. New York:Springer- Verlag,1985.
174 Walczak B, Massart D L. Rough sets theory [J]. Chemometrics and Intelligent Laboratory Systems,1999,47(1):1-16.
175吴健荣.广义系统的二次稳定与二次镇定[J].物理学报,2004,53(2)：325-330.
176 Xiao J, Zhang S, Xu X H. A weighted fuzzy control of double inverted pendulum [A]. Proceeding of the Third Asian Control Conference[C]. Shanghai,2000:1604-1607.
177 Xie G M,Wang L. Controllability of linear descriptor systems [J]. IEEE Trans-actions on circuits and systems-I:fundamental theory and applications,2003, 50(3),455-460.
178谢希仁.计算机网络[M].北京：电子工业出版社,2003.
179谢湘生,刘洪伟.滞后广义系统反馈镇定控制器设计的LMI方法[J].系统工程与电子技术,2000,22(11)：35-38.
180 Xi L, E de Souza. Delay-dependent robust stability and stabilization of uncer-tain linear delay systems:A linear matrix inequality approach[J]. IEEE Trans-actions on Automatic control 1997,42(8):1144-1148.
181 Xi N, Tarn T J. Planning and control of Internet-based teleoperation [A]. Pro-ceedings of SPIE (vo.1 3524) [C]. Bellingham, WA, USA:SPIE,1998:189-195.
182 Xu S Y, Paul Van Dooren, Radu Stefan, and James Lam. Robust Stability and Stabilization for Singular Systems with state delay and parameter uncertainty[J]. IEEE Transactions on Automatic Control,47(7):1122-1128.
183 Yan Chen, Guangren Duan. Conditions for C-controllability and C-observability of Rectangular Descriptor Systems[A]. Proceedings of the 6th World Congress on Intelligent Control and Automation Dalian, China[C].2006:628-630.
184 Yang G H, Zhang S Y. Stabilizing controllers for uncertain symmetric composite systems [J]. Automatica,1995,31(2):337-340.
185 Yang G H, Zhang S Y. Structural Properties of large-scale systems possessing similar structures [J]. Automatica,1995,31(7):1011-1017.
186 Jian-xiong Yang, Dong-yun Lin, Mao-qing Li. Analysis on Controllability of De-scriptor Systems under Structural Decompositions [A]. IEEE International Con-ference on Control and Automation Guangzhou, CHINA[C].2007:3169-3172.
187杨业,王永骥.一类多包传输网络控制系统的设计及稳定性分析[J].信息与控制,2005,34(2)：129-132.
188颜昕,李腊元.NS的仿真机制及协议扩展[J].武汉理工大学学报(交通科学与工程版),2004,28(2)：182-185.
189 Yan X G, Dai. G Z. Decentralized output feedback robust control for nonlinear large-scale systems[J]. Automatica,1998,34(11):1469-1472.
190 Yao Y Y, Lin T Y. Generalization of rough sets using modal logics [J]. Intelligent Automation and Soft Computing,1996,2(2):103-120.
191叶东毅.变精度属性约简及其在决策表规则提取中的应用[J].福建金融管理干部学院学报,2003,75(4),51-54.
192苑明哲,于海斌,周悦.并行计算在网络化控制中的机遇与挑战[J].信息与控制,2003,32(2)：97101,107.
193 Yue D, Han Q L, Lam J. Network-based robust control of systems with uncer-tainty [J]. Automatica,2005,41:999-1007.
194 Yu M, Xie G M, Wang L. Stabilization ofnetworked control systems with trans-mission delays [A]. Proceedings of the IEEE InternationalConference on Systems, Man and Cybernetics [C]. Piscataway, NJ, USA:IEEE,2004:1764-1769.
195张秋红,李玉忍.用MATLAB制作图形用户界面[J].电脑开发与应用.2003,10(16)：10-13.
196张巍,蔡启仲,罗文广MATLAB在自动控制原理实验方面的应用[J].广西工学院学报1999,10(4)：50-53.
197张先明,吴敏,何勇.线性时滞广义系统的时滞相关稳定性[J].电路与系统学报,2003,8(4)：3-7.
198郑大钟.线性系统理论[M].清华大学出版社,2003：114-118.
199 Zhang Q, Han Z X, Wen F S. A new approach for fault diagnosis in power systems based on rough set theory [J]. Proceedings of APSCOM'97, Hong Kong, 1997,597-602.
2张庆灵,张雪峰,翟丁.控制理论基础[M].北京：高等教育出版社,2008.
3陈翰馥.控制理论的现状及对它的期望[J].信息与控制,1994,23(1)：34-37.
4 Zhang Q L, Liu W Q, David H. A Lyapunov approach to analysis of disctete singular systems [J]. Systems and Control Letters,2002,45:237-247.
5冯纯伯.自动控制学科的基础性研究课题[J].东南大学学报,1995,25(4)：22-29.
6 Dai L. Singular control systems[M]. Berlin:Spring-Verlag,1989.
7张庆灵.广义大系统的分散控制与鲁棒控制[M].西安：西北工业大学出版社,1997.
8熊军林,张庆灵.不确定广义系统的最优保成本控制[J].自动化学报,2004,30(4)：588-591.
9杨冬梅,张庆灵.广义系统[M].北京：科学出版社,2004.
10张庆灵,戴冠中,徐心和,等.离散广义系统稳定性分析与控制的Lyapunov方法[J].自动化学报,1998,24(5)：622-629.
11白玫.智能控制理论综述[J].华北水利水电学院学报,2002,23(1)：58-62.
12孙增圻.智能控制理论与技术[M].北京：清华大学出版社,1997.
13 Zadeh L A. Fuzzy set[J]. Information and Control,1965,8:338-358.
14郝丽娜,王伟,吴光宇,等.粗糙集-神经网络故障诊断方法研究[J].东北大学学报：自然科学版,2003,24(3)：252-255.
15 Malyaves V, Savkin A V. The problem of optimal robust Kalman state estimation via limited capacity digital communication channels [J]. Systems and Control Letters,2005,54:285-292.
16俞立.鲁棒控制-线性矩阵不等式处理方法[M].北京：清华大学出版社,2002.
17王国军,陈松乔.自动控制理论发展综述[J].微型机与应用,2000,(6)：4-6.
18 Tom M M机器学习[M].北京：机械工业出版社,2003.
19 Pawlak Z. Rough sets[J]. International Journal of Information and Computer Science,1982, (11):341-356.
20韩祯祥,张琦,文福拴.粗糙集理论及其应用综述[J].控制理论与应用,1999,16(2)：153-157.
21 Yasdi. Rough sets learning and neural learning method to deal with uncertain and imprecise information [J]. Neurocomputing,1995,7(1):61-84.
22曾黄麟.粗集理论及其应用[M].重庆：重庆大学出版社,1998.
23 Golan R and Ziarko W. Methodology for stock market analysis utilizing rough set theory[J]. Proc. of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, New Jersey,1995,32-40.
24 Wong S K M, Ziarko W. On optimal decision rules in decision tables[J]. Bulletin of Polish Academy of Sciences,1985,33(12):694-696.
25 Lin T Y. Rough logic formalism for fuzzy logic controllers-a hard and soft com-puting approach[J]. Journal of Approximate Reasoning,1996,15(4):395-414.
26 Plonka L and Mrozek A. Rule based stabilization of the inverted pendulum [J]. Computational Intelligence,1995,11(2):348-356.
27 Peters J F, Ziaei K, Ramanna S. Approximate time rough control:concepts and application to satellite attitude control.Proc of RSCTC 98, warsaw, poland, 1998,491-498.
28谢克明,杨静.粗糙集理论及其在智能控制领域的应用前景[J].太原理大学学报,1999,30(4)：338-342.
29郭宇殊.粗糙控制中的数据预处理[J].矿业工程,2008,8(3)：64-67.
30郑光勇,叶为全,李斌,庄镇泉.基于粗糙集的过程控制规则挖掘算法及应用[J].微电子学与计算机,2006,23(6)：84-87.
31袁兵,江丽,朱宏辉.基于粗糙集理论的模糊控制规则的获取方法[J].武汉理工大学学报,2005,29(3)：453-455.
32邓九英,毛宗源,杜启亮,谭光兴.基于粗糙集的确定性控制规则决策模型[J].计算机工程,2008,34(10)：166-170.
33秦元勋,王慕秋,王联.运动稳定性理论与应用[M].北京：科学出版社,1981.
34 Yoshizawa T稳定性理论与周期解的存在性[M].郑祖庥译.南宁：广西人民出版社,1987.
35苏晓明,张庆灵.广义周期时变系统[M].北京：科学出版社,2006.
36 Sidi M J. Spacecraft dynamics and control[M]. Cambridge:Cambridge University Press,1997.
37章仁为.卫星轨道姿态动力学与控制[M].北京航空航天大学出版社,1998.
38张庆灵,杨冬梅.不确定广义系统的分析与综合[M].沈阳：东北大学出版社,2003.
39王战平,赵春.一类周期种群系统的稳定性分析及最优控制问题[J].生物数学学报,2008,23(2)：225-230.
40施文武,严洪森,汪峥.一种多周期随机需求生产/库存控制方法[J].控制与决策,2007,22(9)：994-999.
41王林泽,赵文礼.用闭环反馈周期脉冲抑制分叉和混沌运动[J].控制理论与应用,2006,23(3)：487-490.
42 Sreedhar J, Dooren P V. Periodic descriptor system:solvability and condition-ability[J]. IEEE Transactions on Automatic Control,1999,44(2):310-313.
43 Yan W Y. Decentralized control techniques in periodically time-varying discrete-time control systems[J]. IEEE Transaction on Automatic Control,1992,37(10): 1644-1648.
44 Vicente H, Ana U. Pole-assignment problem for discrete-time linear periodic systems [J]. International Journal of Control,1987,46(2):687-697.
45 Bose T, Chen M Q, Joo K S, Xu G F. Stability of two-dimensional discrete sys-tems with periodic coefficients [J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications. II:Analog Dig. Signal Process,1998, 45(7):839-847.
46 Bittanti S, Colaneri P, Guardabassi G. H-controllability and observability of linear periodic systems [J]. SIAM J.Control Optim,22(6):889-893.
47张棣,赵晓强,高占海.空间周期解的理论与应用[J].南京大学学报(数学半年刊),1987,21(1)：37-49.
48王慕秋,王联,吕绍明.关于大系统周期解的存在性[J].科学通报,1987,(13)：972-975.
49陈文成.动力系统的近周期性[J].中国科学(A辑),1995,25(4)：344-348.
50梁家荣,商立群,商立军.时变广义线性系统周期解的存在性[J].2000,30(6)：
51梁家荣,刘永清.广义系统的周期解[J].控制理论与应用,1997,14(4)：595-598.
52 Bamieh B, Pearson J, Francis B, Tannenbaum A. A lifting technique for linear periodic systems[J]. Systems & Control Letters,1991,17(2):79-88.
53 Yamamoto Y. New approach to sampled-data control systems-a function space method[C]. Proceedings of the 29th conference on decision and control, Honolulu, HW 1990,1882-1887.
54 Hu L S, Cao Y, Shao H. Constrained robust sampled-data control for nonlinear uncertain systems[J]. International Journal of Robust and Nonlinear Control, 2002,12(5):447-464.
55汤玉东,邹云.线性离散周期奇异系统的可解性与渐进稳定性[J].控制理论与应用,2004,21(4)：614-616.
56 Yame J J, Hanus R. On stabilization and spectrum assignment in periodically time-varying continuous-time systems [J]. IEEE Transactions on Automatic Con-trol,2001,46:979-983.
57 Kabamba P T. Monodromy eigenvalue assignment in linear periodic aystems[J]. IEEE Transactions on Automatic Control,1986,31(10):950-952.
58王平,李铁寿,吴宏鑫.线性周期系统特征值指数的配置[J].自动化学报,2004,30(4)：530-538.
59陈叔平.关于周期线性系统的能控性和能稳定性[J].高校应用数学学报,1990,1(5)：111-114.
60 Hewer, G. A. Periodicity, detectability and the matrix Riccati equation, SIAM [J]. Control Optim,1975,13(5):1235-1251.
61 Guo G, Qiao J F, Han C Z. Controllability of periodic systems:continuous and discrete[J]. IEE proc.Control Theory Appl,151(4):488-490.
62 Colaneri P, Kucera V. The model matching problem for periodic discrete-time systems[J]. IEEE Transactions on Automatic Control,1997,42(10):1472-1476.
63 Joseph B, Jamel F, Harry H, et al.Stability of fast periodic systems with time lags[J]. IEEE Transactions on Automatic Control,1989,34(4):462-465.
64陈阳舟.周期时变线性系统的一般线性二次型最优控制[J].控制理论与应用.2002,19(4)：415-418.
65 Liu H P, Daniel W C, Ho, Sun F C. A constructive approach to approximate linear periodic systems[J]. IEEE Transactions on Automatic Control,2007,52(3): 541-546.
66谈侃,王朝珠.线性时变周期系统的鲁棒稳定及比控制[J].自动化学报,1996,22(5)：611-614.
67翁爱治.二维周期系统的指数型一致渐进稳定[J].福州大学学报,2004,32(1)：6-34.
68陈喆,王宏禹,邱天爽.适用于LPTV系统的周期自适应滤波器的研究[J].电子与信息学报,2003,25(7)：884-891.
69 Campell S L, Terrel W J. Observability for linear time-varying descriptor system. SIAM Matrix Analysis[J]. Application,1991,12(4):484-496.
70 Bassam A, Bamieh J, Pearson B. A general framework for linear periodic sys-tems with applications to H∞ sampled-data control[J]. IEEE Transactions on Automatic Control,1992,37(4):418-435.
71 S. Lall and G. Dullerud. An LMI solution to the robust synthesis problem for multi-rate sampled-data systems[J].Automatica.2001,37:1909-1922.
72 Brunovsky P. Controllability and linear closed-loop controls in linear periodic systems[J]. Differ. Equ.1969,6(2):296-313.
73 Farhood M, Beck C L, Dullerud G E. Model reduction of periodic systems:A lifting approach[J]. Automatica,2005,41:1085-1090.
74 Gad E, Nakhla M. Efficient model reduction of linear periodically time-varying systems via compressed transient system function [J]. IEEE Transactions on Cir-cuits and Systems-Ⅰ:Fundamental Theory and Applications. I:Reg. Papers,2005, 52(6):1188-1204.
75 Duverrdier A, Lacaze B. On the use of periodic clock changes to implement linear periodic time-varying filters[J]. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications. Ⅱ:Analog Dig. Signal Process,2000, 47(11):1152-11159.
76 Zhang P, Ding S X, Wang G Z, Zhou D H. Fault detection of linear discrete-time periodic systems[J]. IEEE Transactions on Automatic Control,2005,50(2): 239-244.
77 de Souza C E, Trofino A. An LMI approach to stabilization of linear discrete-time periodic systems[J]. International Journal of Control,2000,73(8):696-703.
78 Wei Y Y, Robert R B. Control of linear discrete-time perodic systems:a de-centralized control approach[J]. IEEE Transactions on Automatic Control,1992, 37(10):1644-1648.
79 Rezai M, Ito M R, Lawrence P D. Modeling and simulation of hybrid control systems by global Petri nets [A]. Proceedings of the 1995 IEEE International Symposium on Circuits and Systems [C]. Piscataway, NJ, USA:IEEE,1995: 908-911.
80岳东,彭晨,HanQL网络控制系统的分析与综合[M].北京：科学出版社,2007.
81 Zhang L Q, Shi Y, Chen T W, et al. A new method for stabilization of networked control systems with random delays [J], IEEE Transactions on Automatic Con-trol,2005,50(8):1177-1181.
82 Walsh G C, Ye H, Bushnell L G. Stability analysis ofnetworked control systems [A]. Proceedings of the 1999 American Control Conference [C]. Piscataway, NJ, USA:IEEE,1999:28762880.
83于之训,蒋平,陈辉堂.具有传输延迟的网络控制系统中状态观测器的设计[J].信息与控制,2000,29(2)：125-130.
84顾洪军.网络控制系统建模及性能分析方法的研究[D].北京：清华大学,2001.
85戴冠中,郑应平.网络化系统及其建模,分析,控制与优化[J].自动化学报,2002,28(增刊)：60-65.
86 Halevi Y, Ray A. Integrated communication and control systems:Part Ⅰ-analysis [J]. Journal ofDynamic Systems, Measurement and Contro,1988,110(4):367-373.
87 Murray R M, Astrom K J, Boyd S P, etal. Future directions in control in an information-rich world [J]. IEEE Control Systems Magazine,2003,23(2):20-33.
88 HALEVIY Y, RAY A. Integrated communication and control systems:part I-analysis[J]. Journal of Dynamic System Measure Control,1998,110(4):367-373.
89 Nilsson J B. Bernhardsson B. Wittenmark. Stochastic Analysis and Control of Real-time Systems with Random Time Delays. Automatica,1998,34(1):57-64.
90 TarnT J, Xi N. Planning and control of internet-based teleoperation [J]. Tele-manipulator and Telepresence Technologies V,1998:189-193.
91 Walsh G C, Ye H. Scheduling of networked control systems[J]. IEEE Control Systems Magazine, vol.21,2001:57-65.
92范明哲,于海斌,周悦.并行计算在网络化控制中的机遇与挑战[J].信息与控制,2003,32(2)：97-101+107.
93 Mei Yu, Guangming Xie, Long Wang. Stabilization of Networked Control Sys-tems with Transmission Delays[J]. IEEE International Conference on Systems, Man and Cybernetics.2004,1764-1769.
94 Wei Feng, Ji-Feng Zhang. Mean square stabilization control of switched systems with stochastic disturbances[C], The 43rd IEEE Conference on Decision and Control,2004.
95 Nilsson J. Real-time Control Systems with Delays[D]. Ph. D. dissertation. Swe-den:Lund Institute of Technology,1998.
96于之训,陈辉堂,王月娟.时延网络控制系统均方指数稳定的研究[J].控制与决策,2000,15(3)：278-281,289.
97 Zhang W, Branicky M S, Phillips S M. stability of Networked Control Systems [J]. IEEE Control Systems Magazine,2001,21 (1):84-99.
98谢林柏,方华京,王华.网络化控制系统的信息调度与稳定性研究[J].控制与决策,2004,19(5)：589-591.
99黎善斌,王智,张卫东,等.网络控制系统的研究现状与展望[J].信息与控制,2003,32(3)：239-244.
100 Nilsson J, Bernhardsson B, W ittenmark B. Stochastic analysis and control of real-time systems with random time delays [J]. Automatica,1998,34(1):57-64.
101 Hespanha J P, Naghshtabrizi P, Xu Y G. A survey of recent results in networked control systems [J]. Proceedings of the IEEE,2007,95(1):138-162.
102 Montestruque L A, Antsaklis P. Stability of model-based networked control sys-temswith time-varying transmission times [J]. IEEE Transactions on Automatic Control,2004,49(9):1562-1572.
103龙承念,代双凤,关新平.网络控制系统的补偿策略[J].吉林大学学报(信息科学版),2004,22(4)：438-443.
104王智,王天然,Song Y Q,等.工业实时通讯网络(现场总线)的基础理论研究与现状(上)[J].信息与控制,2002,31(2)：146152,163.
105 Tipsuwan Y, Chow M Y. Controlmethodologies in networked control systems [J]. ControlEngineering Practice,2003,11(10):1099-1111.
106 Lincoln B, Bernhardsson B. Optimal control over networks with long random delays [A]. Proceedings of the InternationalSymposium on Mathematical Theory of Networks and Systems [C]. France:University of Perpignan,2000:1-7.
107 Lin H, Zhai G, Fang L, etal. Stability and H∞performance preserving schedul-ing policy fornetworked control systems [A]. Proceedings of the 16th IFAC World Congress on Automatic Control [C]. Prague, Czech:ElsevierScience,2005.
108 Nilsson J. Real-time ControlSystemswith Delays [D]. Sweden:Lund Institute ofTechnology,1998.
109 N. B. Almutairi. Adaptive Fuzzy Modulation for Networked PI Control Systems. Ph. D. dissertation,2002.
110 Huo Z H, Fang H J. Fault-tolerant control research for networked control system under communication constraints [J]. Acta Automatica Sinica,2006,32(5):659-666.
111朱其新,胡寿松.网络控制系统的能控性和能观性[J].控制与决策,2004,19(2)：157-161.
112 Feng W, Zhang J F. Mean square stabilization controlof switched systemswith stochastic disturbances [A]. Proceedingsof the 43rd IEEE Conference on Decision and Control [C]. Piscataway, NJ, USA:IEEE,2004:3714-3719.
113 Slowinski R. Intelligent decision support-handbook of applications andad-vances of the rough sets theory[M]. Dordrecht:Kluwer Academic Publishers, 1992.
114张文修,吴伟志.粗糙集理论介绍和研究综述[J].模糊系统与数学,2000,14(4)：1-12.
115 Wygralak M. Rough sets and fuzzy sets-some remarks on interrelations[J]. Fuzzy Sets and Systems,1989,29(3):241-240.
116 Nanda S et al. Fuzzy rough sets[J]. Fuzzy Sets and Systems,1992,45(2):157-160.
117 Banerjee M and Pal S K.Roughness of a fuzzy set. Information Sciences,1996, 93(3,4):235-241.
118 Skowton A et al. From rough set theory to evidence theory. Advances in the Dempster Shafer Theory of Evidence[J]. New York:John Wiley and Sons Inc. 1994,193-236.
119 Nejman D. A rough set based method of handwritten numerals classification[M]. Institute of Computer Science Reports, Warsaw University of Technology, War-saw,1994.
120 TeghemJ et al. Use of rough sets method to draw premonitory factors for earthquakes by emphasizing gas geochemistry. In:Intelligent Decision Support-Handbook of applications and Advances of the Rough Sets Theory [J]. Dordrecht: Kluwer Academic Publishers,1992,165-179.
121 Deja R. Conflict model with negotiations.In:Institute of Computer Science Re-ports[M]. Warsaw University of Technlolgy, Warsaw,1995.
122 Hu Xiaohua et al. Mining knowledge rules from databases-a rough set ap-proach[J]. Proc. of IEEE International Conference on Data Engineering, Los Alamitos,1996,96-105.
123 Tsumoto S et al. Extraction of domain knowledge from databases based on rough set theory[J]. IEEE International Conference on Fuzzy Systems, New Jer-sey,1996,748-754.
124 Tsumoto S et al. Automated discovery of Medical expert system rules from clinical databases based on rough sets [J]. Proc. of Second International Conf. on Knowledge Discovery and Data Mining, USA,1996,63-72.
125 Jelonek J et al. Rough set reduction of attributes and their domains for neural networks [J]. Computational Intelligence,1995,11(2):339-347.
126 Peng C et al. Multivalued neural network and the knowledge acquisition method by the rough sets for ambiguous recognition problem[J]. Proc. of the IEEE Inter-national Conference on Systems, Man and Cybernetics, Beijing,1996,736-740.
127 Yasdi R. Combining rough sets learning and neural Iearning2method to deal with uncertain and imprecise information[J]. Neurocomputing,1995,7(1):61-84.
128 Slowinski R. Rough set approach to decision analysis[J]. AI Expert, March 1995, 19-25.
129 Slowinski R et al. Rough set sorting of firms according to bankruptcy risk[J]. In:Applying Multiple Criteria aid for Decision to Environment Management, Dordrecht:Kluwer Academic Publishers,1994,339-357.
130 Slowinski R et al. Rough set reasoning about uncertain data[J]. Fundamenta Informaticae,1996,27(2,3):229-243.
131 Parsons S et al. A rough set approach to reasoning under uncertainty[J]. Journal of Exprimental and Theoretical AI,1995,7(2):175-193.
132 Ruhe G and Gesselschaft F. Rough set based data analysis in goal2oriented soft-ware measurement[J]. Proc.of IEEE International software Metrics Symposium, Los Alamitos,1996,10-19.
133 Wojcik Z et al. Application of rough sets for edge enhancing image filters [J]. Proc. of IEEE International Conference on Image Processing, Los Alamitos, 1994,525-529.
134 Jackson A et al.Rough sets applied to materials data[J]. Acta Materialia,1996, 44(11):4475-4484.
135 Collette T and Szladow A.Use rough sets and spectral data for building pre-dictive models of reaction rate constants[J]. Applied Spectroscopy,1994,48(11): 1379-1386.
136 Aijun A et al.Discovering rules for water demand prediction-an enhanced rough set approach[J]. Engineering Applications of Artificial Intelligence,1996,9(6): 645-653.
137 Wojcik Z et al.Structural modeling using rough sets[J]. Proc.of IEEE Interna-tional Conference on Fuzzy Systems, New Jersey,1996,761-766.
138 Nurmi H et al. Probabilistic,fuzzy and rough concepts in social choice[J].European Journal of Operational Research,1996,95(2):264-277.
139 Lambert Torres G et al.Data Mining into a Control Center Database via Rough Set Techniques [J]. Proc.of the International Conference on Intelligent Systems Applications to Power Systems(ISAP'97), Seoul,1997,246-250.
140张琦,韩祯祥,文福拴.一种基于粗糙集方法的电力系统故障诊断／警报处理的新方法[J].中国电力,1998,31(4)：32-38.
141王珏,苗夺谦,周育键.关于Rough Set理论与应用的综述[J].模式识别与人工智能,1996,9(4)：337-344.
142庾慧英,刘文奇.变精度粗糙集模型中取值范围的确定[J].昆明理工大学学报(理工版),2005,20(6),109-111.
143张雪峰,石凡等,粗糙集数据分析系统的程序实现[J].辽宁石油化工大学学报,200424(3)：66-70.
144 Saaty T L. A scaling method for priorities in hierarchical structures[J]. Journal of Mathematical Psychology,1977,15(3):234-238.
145张雪峰,张庆灵.粗糙集数据分析系统MATLAB仿真工具箱设计[J].东北大学学报：自然科学版,2007,28(1)：40-43.
146赵晨,诸静.过程控制中的一种数据挖掘算法[J].武汉大学学报(工学版),2005,38(5)：131-134.
147宋申民,陈兴林,段广仁.基于粗糙集理论与进化计算的时滞系统Smith控制[J].系统仿真学报,2006,18(8)：2247-2249.
148张倩生.基于粗-模糊神经网络的决策控制[J].控制理论与应用,2005,22(2)：330-334.
149李炜,谢刚,谢克明.一种改进型的粗糙-神经网络PID控制器设计[J].太原理工大学学报,2004,35(3)：251-253.
150赛英,陈伟.从不一致例子中挖掘规则的粗集方法MIE-RS[J]计算机工程与应用,2000,10：22-23.
151赵卫东,盛昭瀚.基于粗集理论的一种归纳学习[J].方法管理工程学报,2000,14(4)：38-42.
152 Nakamura A. A rough logic based on incomplete information and its application [J]. International Journal of Approximate Reasoning,1996,15:367-378.
153 Marzena Kryszkiewicz. Rough set approach to incomplete information sys-tems[J]. Information science,112,1998, pp:39-49.
154 Shan N. An incremental learning algorithm for constructing decision rules [M]. Technical CS-93-02,Dept. of Comp. Sci. Univ. of Regina, Canada,1993.
155 Shan N,Ziarko W. Data—based acquisition and incremental modification of classification rules[J]. Computational Intelligence,1995,11:357-370.
156 Tong Lingyun, An Liping. Incremental learning of decision rules based on rough set theory [J]. Intelligent control and automation,2002, Proc. of the 4th world congress on intelligent control and automation,2002, Shanghai, China, pp:420-425.
157 J. W. Grzymala—Busse. LERS:a system for learning from examples based on rough sets. In:Slowinski, R. (ed.):Intelligent decision support [J]. Handbook of applications and advances of rough sets theory. Kluwer Academic Publishers, Boston,1992, pp:3-18.
158 Sienkiewicz J. Rough set and rough function approaches to the control algorithm reconstruction[M]. Institute of Computer Science Reports, Warsaw University of Technology, Warsaw,1996.
159 Mrozek A et al. Methodology of rough controller synthesis[J]. Proc. of IEEE International Conference on Fuzzy Systems, New Jersey,1996,1135-1139.
160 Czogala E et al. Idea of a rough fuzzy controller and its application to the stabilization of a pendulumcar system[J]. Fuzzy Sets and systems,1995,72(1): 261-273.
161 Arima M et al. Fuzzy logic and rough sets controller for HVAC systems[J]. Proc. of IEEE WESCANEX Communications, Power, and Computing, New York, 1995,133-138.
162张雪峰,宋文安.具有周期T的线性时变系统的稳定性[J].全国青年管理科学与系统科学论文集,1991,1(1)：534-538.
163仝茂达.线性系统理论和设计[M].合肥：中国科学技术大学出版社,2004.
164唐万生,李光泉.广义系统的能控,能观性判别条件[J].自动化学报,1995,21(1):63-66.
165 Petersen I R. A stabilization algorithm for a class of uncertain linear sys-tems [J]. Systems & Control Letters,1987,8:351-357.
166 Petersen I R, McFarlane D C. Optimal guaranteed cost control and filtering for uncertain linear systems [J]. IEEE Transactions on Automatic Control,1994, 39(9):1971-1977.
167 Campbell S L. Singular systems of differentials equations[M]. pitman advanced publishing program, Sanfrancisco London Melbourne,1980.
168 H. M. AI-Ramani, G. F. Franklin. Linear Periodic systems:Eigenvalue assign-ment using discrete periodic feedback[J]. IEEE Tras.Automat. Contr.1989,34: 99-103.
169 S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory[M]. SIAM Studies in Applied Mathematics. SIAM, Philadelphia, Pennsylvania,1994.
170 R. Datko.Solutions of the operator equation A* K+KA+KRK=-W. In: Semigroups of Operators:Theory and Applications. A. V. Balakrishnan, Ed. Birkhauser,2000.
171 Vincent D. Blondel, Alexandre Megretski. Unsolved Problems in Mathematical Systems and Control Theory[M]. New Jersey, USA:Princeton University,2004.
172 G. R. Duan, G. W. Irwin, G. P. Liu. Roubust Stabilization of Descriptor Linear Systems via Proportional-plus-derivative State Feedback.Proceedings of Ameri-can Control Conference San Diego, Califormia.1999,6:1304-1308.
173 Wohnam W M. Linear Multivariable Control:A Geometric Approach,3rd edn[M]. New York:Springer- Verlag,1985.
174 Walczak B, Massart D L. Rough sets theory [J]. Chemometrics and Intelligent Laboratory Systems,1999,47(1):1-16.
175吴健荣.广义系统的二次稳定与二次镇定[J].物理学报,2004,53(2)：325-330.
176 Xiao J, Zhang S, Xu X H. A weighted fuzzy control of double inverted pendulum [A]. Proceeding of the Third Asian Control Conference[C]. Shanghai,2000:1604-1607.
177 Xie G M,Wang L. Controllability of linear descriptor systems [J]. IEEE Trans-actions on circuits and systems-I:fundamental theory and applications,2003, 50(3),455-460.
178谢希仁.计算机网络[M].北京：电子工业出版社,2003.
179谢湘生,刘洪伟.滞后广义系统反馈镇定控制器设计的LMI方法[J].系统工程与电子技术,2000,22(11)：35-38.
180 Xi L, E de Souza. Delay-dependent robust stability and stabilization of uncer-tain linear delay systems:A linear matrix inequality approach[J]. IEEE Trans-actions on Automatic control 1997,42(8):1144-1148.
181 Xi N, Tarn T J. Planning and control of Internet-based teleoperation [A]. Pro-ceedings of SPIE (vo.1 3524) [C]. Bellingham, WA, USA:SPIE,1998:189-195.
182 Xu S Y, Paul Van Dooren, Radu Stefan, and James Lam. Robust Stability and Stabilization for Singular Systems with state delay and parameter uncertainty[J]. IEEE Transactions on Automatic Control,47(7):1122-1128.
183 Yan Chen, Guangren Duan. Conditions for C-controllability and C-observability of Rectangular Descriptor Systems[A]. Proceedings of the 6th World Congress on Intelligent Control and Automation Dalian, China[C].2006:628-630.
184 Yang G H, Zhang S Y. Stabilizing controllers for uncertain symmetric composite systems [J]. Automatica,1995,31(2):337-340.
185 Yang G H, Zhang S Y. Structural Properties of large-scale systems possessing similar structures [J]. Automatica,1995,31(7):1011-1017.
186 Jian-xiong Yang, Dong-yun Lin, Mao-qing Li. Analysis on Controllability of De-scriptor Systems under Structural Decompositions [A]. IEEE International Con-ference on Control and Automation Guangzhou, CHINA[C].2007:3169-3172.
187杨业,王永骥.一类多包传输网络控制系统的设计及稳定性分析[J].信息与控制,2005,34(2)：129-132.
188颜昕,李腊元.NS的仿真机制及协议扩展[J].武汉理工大学学报(交通科学与工程版),2004,28(2)：182-185.
189 Yan X G, Dai. G Z. Decentralized output feedback robust control for nonlinear large-scale systems[J]. Automatica,1998,34(11):1469-1472.
190 Yao Y Y, Lin T Y. Generalization of rough sets using modal logics [J]. Intelligent Automation and Soft Computing,1996,2(2):103-120.
191叶东毅.变精度属性约简及其在决策表规则提取中的应用[J].福建金融管理干部学院学报,2003,75(4),51-54.
192苑明哲,于海斌,周悦.并行计算在网络化控制中的机遇与挑战[J].信息与控制,2003,32(2)：97101,107.
193 Yue D, Han Q L, Lam J. Network-based robust control of systems with uncer-tainty [J]. Automatica,2005,41:999-1007.
194 Yu M, Xie G M, Wang L. Stabilization ofnetworked control systems with trans-mission delays [A]. Proceedings of the IEEE InternationalConference on Systems, Man and Cybernetics [C]. Piscataway, NJ, USA:IEEE,2004:1764-1769.
195张秋红,李玉忍.用MATLAB制作图形用户界面[J].电脑开发与应用.2003,10(16)：10-13.
196张巍,蔡启仲,罗文广MATLAB在自动控制原理实验方面的应用[J].广西工学院学报1999,10(4)：50-53.
197张先明,吴敏,何勇.线性时滞广义系统的时滞相关稳定性[J].电路与系统学报,2003,8(4)：3-7.
198郑大钟.线性系统理论[M].清华大学出版社,2003：114-118.
199 Zhang Q, Han Z X, Wen F S. A new approach for fault diagnosis in power systems based on rough set theory [J]. Proceedings of APSCOM'97, Hong Kong, 1997,597-602.