Stochastic observer design for Markovian jump one-sided Lipschitz systems with partly unknown transition rates
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- 英文论文题名：Stochastic observer design for Markovian jump one-sided Lipschitz systems with partly unknown transition rates
- 论文作者：Shangwen Xia ; Shaohua Ma ; Zhiyuan Cai ; Zhifeng Zhang
- 英文论文作者：Shangwen Xia ; Shaohua Ma ; Zhiyuan Cai ; Zhifeng Zhang ; School of Electrical Engineering ; Shenyang University of Technology
- 年：2017
- 作者机构：School of Electrical Engineering,Shenyang University of Technology;
- 英文论文关键词：Stochastic observer ; One-sided Lipschitz systems ; Markovian jump ; Partly unknown transition rates
- 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：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：6
- 文件大小：231k
- 原文格式：D
- 会议级别：全国
摘要
This paper deals with the stochastic observer design problem for the Markovian jump one-sided Lipschitz system with partly unknown transition rates. Firstly, the definitions as well as properties of one-sided Lipschitz function are introduced.Then, the observer is constructed for the system by Luenberger observer theory and the existence condition of the observer is derived by linear matrix inequality technique. Finally, two numerical examples are simulated to verify the effectiveness of the proposed method in this paper.
This paper deals with the stochastic observer design problem for the Markovian jump one-sided Lipschitz system with partly unknown transition rates. Firstly, the definitions as well as properties of one-sided Lipschitz function are introduced.Then, the observer is constructed for the system by Luenberger observer theory and the existence condition of the observer is derived by linear matrix inequality technique. Finally, two numerical examples are simulated to verify the effectiveness of the proposed method in this paper.
This paper deals with the stochastic observer design problem for the Markovian jump one-sided Lipschitz system with partly unknown transition rates. Firstly, the definitions as well as properties of one-sided Lipschitz function are introduced.Then, the observer is constructed for the system by Luenberger observer theory and the existence condition of the observer is derived by linear matrix inequality technique. Finally, two numerical examples are simulated to verify the effectiveness of the proposed method in this paper.
引文
[1]G.Hu,Observers for one-sided Lipschitz non-linear systems,IMA Journal of Mathematical Control and Information,23:395-401,2006.
[2]G.Hu,A note on observer for one-sided Lipschitz non-linear systems,IMA Journal of Mathematical Control and Information,25:297-303,2008.
[3]Y.Zhao,J.Tao and N.Shi,A note on observer design for onesided Lipschitz nonlinear systems,Systems&Control Letters,59:66-71,2010.
[4]M.Abbaszadeh and H.Marquez,Nonlinear observer design for one-sided Lipschitz systems,in Proceedings of the American Control Conference,2010:5284-5289.
[5]W.Zhang,H.Su,Y.Liang and Z.Han,Non-linear observer design for one-sided Lipschitz systems:an linear matrix inequality approach,IET Control Theory&Applications,6:1297-1303,2012.
[6]W.Zhang,H.Su,F.Zhu and D.Yue,A Note on Observers for Discrete-Time Lipschitz Nonlinear Systems,IEEE Transactions on Circuits&Systems II,59:123-127,2012.
[7]M.Benallouch,M.Boutayeb and M.Zasadzinski,Observer design for one-sided Lipschitz discrete-time systems,Systems&Control Letters,61:879-886,2012.
[8]W.Zhang,H.Su,F.Zhu and G.Azar,Unknown input observer design for one-sided Lipschitz nonlinear systems,Nonlinear Dynamics,79:1469-1479,2015.
[9]M.Nguyen and H.Trinh,Unknown input observer design for one-sided Lipschitz discrete-time systems subject to timedelay,Applied Mathematics and Computation,286:57-71,2016.
[10]L.Li,Y.Yang,Y.Zhang and S.Ding,Fault estimation of one-sided Lipschitz and quasi-one-sided Lipschitz systems,in Chinese Control Conference,2014:2574-2579.
[11]X.Cai,Y.Lin and S.Hong,Stabilisation for one-sided Lipschitz non-linear differential inclusions,IET Control Theory&Applications,7:2172-2177,2013.
[12]X.Cai,Z.Wang and L.Liu,Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay,Neurocomputing,165:182-189,2015.
[13]H.Beikzadeh and H.Marquez,Observer-based H∞control using the incremental gain for one-sided Lipschitz nonlinear systems,in American Control Conference,2014:4653-4658.
[14]Y.Dong,W.Liu,S.Liang,Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties,International Journal of Robust&Nonlinear Control,DOI:10.1002/rnc.3648,2016.
[15]W.Zhang,H.Su,F.Zhu,S.Bhattacharyya.Improved exponential observer design for one-sided Lipschitz nonlinear systems,International Journal of Robust&Nonlinear Control,26:3958-3973,2016.
[16]L.Wu,X.Su and P.Shi,Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems,Automatica,48:1929-1933,2010.
[17]Y.Kao,J.Guo,C.Wang and X.Sun,Delay-dependent robust exponential stability of Markovian jumping reactiondiffusion Cohen-Grossberg neural networks with mixed delays,Journal of Franklin Institute,349:1972-1988,2012.
[18]Y.Xia,L.Li,M.Mahmoud and H.Yang,H∞filtering for nonlinear singular Markovian jumping systems with interval time-varying delays,International Journal of Systems Science,43:351-361,2012.
[19]J.Wang,H.Wang,A.Xue and R.Lu,Delay-dependent H∞control for singular Markovian jump systems with time delay,Nonlinear Analysis:Hybrid Systems,8,1-12,2013.
[20]L.Zhang,E.Boukas and J.Lam,Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities,IEEE Transactions on Automatic Control,53:2458-2462,2008.
[21]L.Zhang and E.Boukas,Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities,Automatica,45:463-468,2009.
[22]Y.Zhang,Y.He,M.Wu and J.Zhang,Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices,Automatica,47:79-84,2011.
[23]D.Zhai,A.Lu,M.Liu and Q.Zhang,H∞control for Markovian jump systems with partially unknown transition rates via an adaptive method,Journal of Mathematical Analysis and Applications,446:886-907,2016.
[24]D.Zhang,Q.Zhang and B.Du,Positivity and stability of positive singular Markovian jump time-delay systems with partially unknown transition rates,Journal of the Franklin Institute,354:627-649,2017.
[25]J.Lin,S.Fei and J.Shen,Delay-dependent H∞filtering for discrete-time singular Markovian jump systems with timevarying delay and partially unknown transition probabilities,Signal Processing,91:277-289,2011.
[26]M.Shen and D.Ye,Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions,Fuzzy Sets and Systems,217:80-95,2013.
[27]R.Li and J.Cao,Finite-Time Stability Analysis for Markovian Jump Memristive Neural Networks With Partly Unknown Transition Probabilities,IEEE Transactions on Neural Networks and Learning Systems,DOI:10.1109/TNNLS.2016.2609148,2016.
[28]J.Zhou,H.Dong and J.Feng,Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates,Applied Mathematics and Computation,293:617-629,2017.
[29]H.Kushner,Stochastic Stability and Control.New York:Academic Press,1967.
[30]S.Raghavan,J.Hedrick,Observer design for a class of nonlinear systems,International Journal of Control,59:515-528,1994.
[2]G.Hu,A note on observer for one-sided Lipschitz non-linear systems,IMA Journal of Mathematical Control and Information,25:297-303,2008.
[3]Y.Zhao,J.Tao and N.Shi,A note on observer design for onesided Lipschitz nonlinear systems,Systems&Control Letters,59:66-71,2010.
[4]M.Abbaszadeh and H.Marquez,Nonlinear observer design for one-sided Lipschitz systems,in Proceedings of the American Control Conference,2010:5284-5289.
[5]W.Zhang,H.Su,Y.Liang and Z.Han,Non-linear observer design for one-sided Lipschitz systems:an linear matrix inequality approach,IET Control Theory&Applications,6:1297-1303,2012.
[6]W.Zhang,H.Su,F.Zhu and D.Yue,A Note on Observers for Discrete-Time Lipschitz Nonlinear Systems,IEEE Transactions on Circuits&Systems II,59:123-127,2012.
[7]M.Benallouch,M.Boutayeb and M.Zasadzinski,Observer design for one-sided Lipschitz discrete-time systems,Systems&Control Letters,61:879-886,2012.
[8]W.Zhang,H.Su,F.Zhu and G.Azar,Unknown input observer design for one-sided Lipschitz nonlinear systems,Nonlinear Dynamics,79:1469-1479,2015.
[9]M.Nguyen and H.Trinh,Unknown input observer design for one-sided Lipschitz discrete-time systems subject to timedelay,Applied Mathematics and Computation,286:57-71,2016.
[10]L.Li,Y.Yang,Y.Zhang and S.Ding,Fault estimation of one-sided Lipschitz and quasi-one-sided Lipschitz systems,in Chinese Control Conference,2014:2574-2579.
[11]X.Cai,Y.Lin and S.Hong,Stabilisation for one-sided Lipschitz non-linear differential inclusions,IET Control Theory&Applications,7:2172-2177,2013.
[12]X.Cai,Z.Wang and L.Liu,Control design for one-side Lipschitz nonlinear differential inclusion systems with time-delay,Neurocomputing,165:182-189,2015.
[13]H.Beikzadeh and H.Marquez,Observer-based H∞control using the incremental gain for one-sided Lipschitz nonlinear systems,in American Control Conference,2014:4653-4658.
[14]Y.Dong,W.Liu,S.Liang,Nonlinear observer design for one-sided Lipschitz systems with time-varying delay and uncertainties,International Journal of Robust&Nonlinear Control,DOI:10.1002/rnc.3648,2016.
[15]W.Zhang,H.Su,F.Zhu,S.Bhattacharyya.Improved exponential observer design for one-sided Lipschitz nonlinear systems,International Journal of Robust&Nonlinear Control,26:3958-3973,2016.
[16]L.Wu,X.Su and P.Shi,Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems,Automatica,48:1929-1933,2010.
[17]Y.Kao,J.Guo,C.Wang and X.Sun,Delay-dependent robust exponential stability of Markovian jumping reactiondiffusion Cohen-Grossberg neural networks with mixed delays,Journal of Franklin Institute,349:1972-1988,2012.
[18]Y.Xia,L.Li,M.Mahmoud and H.Yang,H∞filtering for nonlinear singular Markovian jumping systems with interval time-varying delays,International Journal of Systems Science,43:351-361,2012.
[19]J.Wang,H.Wang,A.Xue and R.Lu,Delay-dependent H∞control for singular Markovian jump systems with time delay,Nonlinear Analysis:Hybrid Systems,8,1-12,2013.
[20]L.Zhang,E.Boukas and J.Lam,Analysis and Synthesis of Markov Jump Linear Systems With Time-Varying Delays and Partially Known Transition Probabilities,IEEE Transactions on Automatic Control,53:2458-2462,2008.
[21]L.Zhang and E.Boukas,Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities,Automatica,45:463-468,2009.
[22]Y.Zhang,Y.He,M.Wu and J.Zhang,Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices,Automatica,47:79-84,2011.
[23]D.Zhai,A.Lu,M.Liu and Q.Zhang,H∞control for Markovian jump systems with partially unknown transition rates via an adaptive method,Journal of Mathematical Analysis and Applications,446:886-907,2016.
[24]D.Zhang,Q.Zhang and B.Du,Positivity and stability of positive singular Markovian jump time-delay systems with partially unknown transition rates,Journal of the Franklin Institute,354:627-649,2017.
[25]J.Lin,S.Fei and J.Shen,Delay-dependent H∞filtering for discrete-time singular Markovian jump systems with timevarying delay and partially unknown transition probabilities,Signal Processing,91:277-289,2011.
[26]M.Shen and D.Ye,Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions,Fuzzy Sets and Systems,217:80-95,2013.
[27]R.Li and J.Cao,Finite-Time Stability Analysis for Markovian Jump Memristive Neural Networks With Partly Unknown Transition Probabilities,IEEE Transactions on Neural Networks and Learning Systems,DOI:10.1109/TNNLS.2016.2609148,2016.
[28]J.Zhou,H.Dong and J.Feng,Event-triggered communication for synchronization of Markovian jump delayed complex networks with partially unknown transition rates,Applied Mathematics and Computation,293:617-629,2017.
[29]H.Kushner,Stochastic Stability and Control.New York:Academic Press,1967.
[30]S.Raghavan,J.Hedrick,Observer design for a class of nonlinear systems,International Journal of Control,59:515-528,1994.