Asynchronous H_∞ Output Feedback Control for a Class of Markov Jump Systems
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- 英文论文题名：Asynchronous H_∞ Output Feedback Control for a Class of Markov Jump Systems
- 论文作者：Xiao Lu ; Lei Yang ; Haixia Wang ; Chunyang Sheng
- 英文论文作者：Xiao Lu ; Lei Yang ; Haixia Wang ; Chunyang Sheng ; College of Electrical Engineering and Automation ; Shandong University of Science and Techology
- 年：2017
- 作者机构：College of Electrical Engineering and Automation,Shandong University of Science and Techology;
- 英文论文关键词：asynchronous H_∞ control ; a set of Markov jump systems ; LMIs ; output feedback
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O211.62;O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：4
- 文件大小：295k
- 原文格式：D
- 会议级别：全国
摘要
This article is concerned with resilient asynchronous H∞ output feedback controller designed for a set of Markov jump linear systems(MJLSs). By Finsler's Lemma, and with the help of two sets of slack variables, the problem of inter connection between the Lyapunov matrices and the system matrices was solved. Resilient asynchronous controller is designed to ensure the controller has the character of robustness and the drawback that the controller can't get the information of the system's mode is overcame. The controller we designed for the closed-loop system not only makes sure the system has a prescribed H∞performance index but also is stochastically stable. The bilinear matrix inequalities(BMIs) are given as the sufficient conditions for the controller design, which can be solved by using linear matrix inequalities(LMIs) along with line search..
This article is concerned with resilient asynchronous H_∞ output feedback controller designed for a set of Markov jump linear systems(MJLSs). By Finsler's Lemma, and with the help of two sets of slack variables, the problem of inter connection between the Lyapunov matrices and the system matrices was solved. Resilient asynchronous controller is designed to ensure the controller has the character of robustness and the drawback that the controller can't get the information of the system's mode is overcame. The controller we designed for the closed-loop system not only makes sure the system has a prescribed H_∞performance index but also is stochastically stable. The bilinear matrix inequalities(BMIs) are given as the sufficient conditions for the controller design, which can be solved by using linear matrix inequalities(LMIs) along with line search..
This article is concerned with resilient asynchronous H_∞ output feedback controller designed for a set of Markov jump linear systems(MJLSs). By Finsler's Lemma, and with the help of two sets of slack variables, the problem of inter connection between the Lyapunov matrices and the system matrices was solved. Resilient asynchronous controller is designed to ensure the controller has the character of robustness and the drawback that the controller can't get the information of the system's mode is overcame. The controller we designed for the closed-loop system not only makes sure the system has a prescribed H_∞performance index but also is stochastically stable. The bilinear matrix inequalities(BMIs) are given as the sufficient conditions for the controller design, which can be solved by using linear matrix inequalities(LMIs) along with line search..
引文
[1]O.Costa,M.Fragoso,R.Marques,Discrete-time Markov Jump Linear Systems,London:Springer-Verlag,2005.
[2]L.X.Zhang,Y.Z.Zhu,P.Shi,Resilient estimation for a class of Markov jump linear systems with unideal measurement and its application to robot arm systems,Proceeding of the 41th Annual Conference of the IEEE Industrial Electronics Society,pp.002515-002520,2015.
[3]Y.J.Zhang,Y.S.Ou,Y.M.Zhou,G.Q.Xu,H∞control of Markov jump systems with time-varying delay and incomplete transition probabilities filtering for discrete-time piecewise homogenous Markov jump systems with application to economic systems,Proceeding of 40th Annual Conference of the IEEE Industrial Electronics Society,pp.176-182,2014.
[4]A.N.Vargas,G.Pujol,L.Acho,Stability of Markov jump systems with quadratic terms and its application to RLC circuits,Journal of the Franklin Institute,vol.354,no.1,pp.332-344,Jan.2017.
[5]O.Costa,M.Fragoso,Stability results for discrete-time linear systems with Markovian jumping parameters,Journal of Mathematical Analysis and Applications,vol.179,no.1,pp.154-178.
[6]A.K.Xue,H.J.Wang,R.Q Lu,Event-based H∞control for discrete Markov jump systems,Neurocomputing,vol.190,pp.165-171,May.2016.
[7]J.R.Chen,F.Liu,Robust reliable H∞control for discretetime Markov jump linear systems with actuator failures,Journal of Systems Engineering and Electronics,vol.19,no.5,pp.965-973,Aug.2008.
[8]X.L.Luan,S.Y.Zhao,F.Liu,H∞control for discrete-time Markov jump systems with uncertain transition probabilities,IEEE Transaction on Automatic Control,vol.58,no.6,pp.1566-1572,2013.
[9]X.N.Song,Y.Z.Men,J.P.Zhou,J.J.Zhao,H.Shen,Eventtriggered H∞control for networked discrete-time Markov jump systems with repeated scalar nonlinearities,Applied Mathematics and Computation,vol.298,no.1,pp.123-132,Apr.2017.
[10]L.C.Li,M.Q.Shen,G.M.Zhang,S.Yan,H∞control of Markov jump systems with time-varying delay and incomplete transition probabilities,Applied Mathematics and Computation,vol.301,pp.95-106,May.2017.
[11]M.Q.Shen,D.Ye,Q.G.Wang,Mode-dependent filter design for Markov jump systems with sensor nonlinearities in finite frequency domain,Signal Processing,vol.134,pp.1-8,May.2017.
[12]Z.G.Wu,H.Y.Su,J.Chu,Delay-dependent H∞filtering for Markov jump time-delay systems,Signal Processing,vol.90,no.6,pp.1815-1824,Jun.2010.
[13]Y.Z.Zhu,L.X.Zhang,W.X.Zheng,Distributed H∞filtering for a class of discrete-time Markov jump Lur’e systems with redundant channels,IEEE Transactions on Industrial Electronics,vol.63,no.3,pp.1876-1885,2016.
[14]Z.G.Wu,P.Shi,H.Su,J.Chu,Asynchronous l2l∞filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities,Automatica,vol.50,no.1,pp.180-186,Jan.2014.
[15]H.Shen,Y.Z.Zhu,L.X.Zhang,J.H.Park,Extended dissipative state estimation for Markov jump nerual networks with unreliable links,IEEE Transation on Nerual Networks and Learing Systems,vol.28,no.2,pp.346-358,2017.
[16]L.X.Zhang,Y.Z.Zhu,P.Shi,Y.X.Zhao,Resilient asynchronous H∞filtering for Markov jump nerual networks with unideal measurements and multiplicative noises,IEEE Transaction on Cybernetics,vol.45,no.12,pp.2840-2852,2015.
[17]M.G.Todorov,M.Fragoso,On the state-feedback robust control of continuous-time infinite Markov jump linear systems,Proceeding of 49th IEEE Conference on Decision and Control,pp.6499-6504,2010.
[18]G.W.Gabrie,M.Souza,H2 state feedback sampled-data control for Markov jump linear systems,Proceeding of 53rd IEEE Conference on Decision and Control,pp.4355-4360,2014.
[19]G.W.Gabrie,K.M.Grigoriadis,Optimal H∞state feedback sampled-data control applied to Markov jump linear systems,Proceeding of 2016 European Control Conference,pp.2489-2494,2016.
[20]Y.Z.Zhu,L.X.Zhang,M.V.Basin,Non stationary H∞dynamic output feedback control for discrete-time Markov jump linear systems with actuator and sensor saturations,International Journal of Robust and Nonlinear Control,pp.1010-1025,Apr.2015.
[21]B.C.Wang,J.F.Zhang,Distributed output feedback control of Markov jump multi-agent systems,Automatica,vol.49,no.5,pp.1397-1402,May.2013.
[22]W.W.Che,J.L.Wang,Static output feedback H∞control for discrete-time Markov jump linear systems,Proceeding of 8th IEEE International Conference on Control and Automation,pp.2278-2283,2010.
[23]D.W.Ding,G.H.Yang,H∞static output feedback control for discrete-time switched linear systems with average dwell time,IET Control Theory and Applications,vol.4,no.3,pp.381-390,2010.
[24]Z.Shu,J.Lam,J.L.Xiong,Static output-feedback stabilization of discrete-time Markovian jump linear systems:A system augmentation approach,Automatica,vol.46,no.4,pp.687-694,Jul 2016.
[25]M.Q.Shen,D.Ye,S.M.Fei,Robust H∞static output control of discrete Markov jump linear systems with norm bounded uncertainties,IET Control Theory and Applications,vol.8,no.15,pp.1449-1455,2014.
[26]W.W.Che,Y.P.Li,Y.L.Wang,Static output feedback H∞control for Markov jump linear systems with random packet losses,Proceeding of 24th Chinese Control Conference,pp.412-416,2012.
[27]L.Xie,Output feedback H∞control of systems with parameter uncertainty,International Journal of Control,vol.63,no.4,pp.741-750,1996.
[28]Z.X.Zhong,Y.Z.Zhu,T.Yang,Robust Decentralized Static Output-Feedback Control Design for Large-Scale Nonlinear Systems Using Takagi-Sugeno Fuzzy Models,IEEE Access,vol.4,pp.8250-8263,2016.
[2]L.X.Zhang,Y.Z.Zhu,P.Shi,Resilient estimation for a class of Markov jump linear systems with unideal measurement and its application to robot arm systems,Proceeding of the 41th Annual Conference of the IEEE Industrial Electronics Society,pp.002515-002520,2015.
[3]Y.J.Zhang,Y.S.Ou,Y.M.Zhou,G.Q.Xu,H∞control of Markov jump systems with time-varying delay and incomplete transition probabilities filtering for discrete-time piecewise homogenous Markov jump systems with application to economic systems,Proceeding of 40th Annual Conference of the IEEE Industrial Electronics Society,pp.176-182,2014.
[4]A.N.Vargas,G.Pujol,L.Acho,Stability of Markov jump systems with quadratic terms and its application to RLC circuits,Journal of the Franklin Institute,vol.354,no.1,pp.332-344,Jan.2017.
[5]O.Costa,M.Fragoso,Stability results for discrete-time linear systems with Markovian jumping parameters,Journal of Mathematical Analysis and Applications,vol.179,no.1,pp.154-178.
[6]A.K.Xue,H.J.Wang,R.Q Lu,Event-based H∞control for discrete Markov jump systems,Neurocomputing,vol.190,pp.165-171,May.2016.
[7]J.R.Chen,F.Liu,Robust reliable H∞control for discretetime Markov jump linear systems with actuator failures,Journal of Systems Engineering and Electronics,vol.19,no.5,pp.965-973,Aug.2008.
[8]X.L.Luan,S.Y.Zhao,F.Liu,H∞control for discrete-time Markov jump systems with uncertain transition probabilities,IEEE Transaction on Automatic Control,vol.58,no.6,pp.1566-1572,2013.
[9]X.N.Song,Y.Z.Men,J.P.Zhou,J.J.Zhao,H.Shen,Eventtriggered H∞control for networked discrete-time Markov jump systems with repeated scalar nonlinearities,Applied Mathematics and Computation,vol.298,no.1,pp.123-132,Apr.2017.
[10]L.C.Li,M.Q.Shen,G.M.Zhang,S.Yan,H∞control of Markov jump systems with time-varying delay and incomplete transition probabilities,Applied Mathematics and Computation,vol.301,pp.95-106,May.2017.
[11]M.Q.Shen,D.Ye,Q.G.Wang,Mode-dependent filter design for Markov jump systems with sensor nonlinearities in finite frequency domain,Signal Processing,vol.134,pp.1-8,May.2017.
[12]Z.G.Wu,H.Y.Su,J.Chu,Delay-dependent H∞filtering for Markov jump time-delay systems,Signal Processing,vol.90,no.6,pp.1815-1824,Jun.2010.
[13]Y.Z.Zhu,L.X.Zhang,W.X.Zheng,Distributed H∞filtering for a class of discrete-time Markov jump Lur’e systems with redundant channels,IEEE Transactions on Industrial Electronics,vol.63,no.3,pp.1876-1885,2016.
[14]Z.G.Wu,P.Shi,H.Su,J.Chu,Asynchronous l2l∞filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities,Automatica,vol.50,no.1,pp.180-186,Jan.2014.
[15]H.Shen,Y.Z.Zhu,L.X.Zhang,J.H.Park,Extended dissipative state estimation for Markov jump nerual networks with unreliable links,IEEE Transation on Nerual Networks and Learing Systems,vol.28,no.2,pp.346-358,2017.
[16]L.X.Zhang,Y.Z.Zhu,P.Shi,Y.X.Zhao,Resilient asynchronous H∞filtering for Markov jump nerual networks with unideal measurements and multiplicative noises,IEEE Transaction on Cybernetics,vol.45,no.12,pp.2840-2852,2015.
[17]M.G.Todorov,M.Fragoso,On the state-feedback robust control of continuous-time infinite Markov jump linear systems,Proceeding of 49th IEEE Conference on Decision and Control,pp.6499-6504,2010.
[18]G.W.Gabrie,M.Souza,H2 state feedback sampled-data control for Markov jump linear systems,Proceeding of 53rd IEEE Conference on Decision and Control,pp.4355-4360,2014.
[19]G.W.Gabrie,K.M.Grigoriadis,Optimal H∞state feedback sampled-data control applied to Markov jump linear systems,Proceeding of 2016 European Control Conference,pp.2489-2494,2016.
[20]Y.Z.Zhu,L.X.Zhang,M.V.Basin,Non stationary H∞dynamic output feedback control for discrete-time Markov jump linear systems with actuator and sensor saturations,International Journal of Robust and Nonlinear Control,pp.1010-1025,Apr.2015.
[21]B.C.Wang,J.F.Zhang,Distributed output feedback control of Markov jump multi-agent systems,Automatica,vol.49,no.5,pp.1397-1402,May.2013.
[22]W.W.Che,J.L.Wang,Static output feedback H∞control for discrete-time Markov jump linear systems,Proceeding of 8th IEEE International Conference on Control and Automation,pp.2278-2283,2010.
[23]D.W.Ding,G.H.Yang,H∞static output feedback control for discrete-time switched linear systems with average dwell time,IET Control Theory and Applications,vol.4,no.3,pp.381-390,2010.
[24]Z.Shu,J.Lam,J.L.Xiong,Static output-feedback stabilization of discrete-time Markovian jump linear systems:A system augmentation approach,Automatica,vol.46,no.4,pp.687-694,Jul 2016.
[25]M.Q.Shen,D.Ye,S.M.Fei,Robust H∞static output control of discrete Markov jump linear systems with norm bounded uncertainties,IET Control Theory and Applications,vol.8,no.15,pp.1449-1455,2014.
[26]W.W.Che,Y.P.Li,Y.L.Wang,Static output feedback H∞control for Markov jump linear systems with random packet losses,Proceeding of 24th Chinese Control Conference,pp.412-416,2012.
[27]L.Xie,Output feedback H∞control of systems with parameter uncertainty,International Journal of Control,vol.63,no.4,pp.741-750,1996.
[28]Z.X.Zhong,Y.Z.Zhu,T.Yang,Robust Decentralized Static Output-Feedback Control Design for Large-Scale Nonlinear Systems Using Takagi-Sugeno Fuzzy Models,IEEE Access,vol.4,pp.8250-8263,2016.
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