Observer-based Static Feedback Control for Neutral-type Markovian Jump Systems
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- 英文论文题名：Observer-based Static Feedback Control for Neutral-type Markovian Jump Systems
- 论文作者：Tianshu Yang ; Jing Xie ; Yunlong Liu ; Yonggui Kao
- 英文论文作者：Tianshu Yang ; Jing Xie ; Yunlong Liu ; Yonggui Kao ; Department of Mathematics ; Harbin Institute of Technology (Weihai) ; College of Automation Engineering ; Qingdao University of Technology ; College of Information and Control Engineering ; Weifang University
- 年：2017
- 作者机构：Department of Mathematics,Harbin Institute of Technology (Weihai);College of Automation Engineering,Qingdao University of Technology;College of Information and Control Engineering,Weifang University;
- 英文论文关键词：Markvian jump system ; static feedback control ; neutral-type ; linear matrix inequality
- 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（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 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：207k
- 原文格式：D
- 会议级别：全国
摘要
This paper is concerned with the state estimation problem of a class of uncertain Markovian jump neutral-type stochastic systems. This kind of systems involves parameter uncertainties, noise disturbances and time-delay. Based on Lyapunov-Krasovskii functional approach, a delay-dependent condition is derived for the existence of state observer. The desired gain matrix and state-feedback controller are presented in terms of linear matrix inequality(LMI). Finally, a numerical example is provided to illustrate the validity of the obtained results.
This paper is concerned with the state estimation problem of a class of uncertain Markovian jump neutral-type stochastic systems. This kind of systems involves parameter uncertainties, noise disturbances and time-delay. Based on Lyapunov-Krasovskii functional approach, a delay-dependent condition is derived for the existence of state observer. The desired gain matrix and state-feedback controller are presented in terms of linear matrix inequality(LMI). Finally, a numerical example is provided to illustrate the validity of the obtained results.
This paper is concerned with the state estimation problem of a class of uncertain Markovian jump neutral-type stochastic systems. This kind of systems involves parameter uncertainties, noise disturbances and time-delay. Based on Lyapunov-Krasovskii functional approach, a delay-dependent condition is derived for the existence of state observer. The desired gain matrix and state-feedback controller are presented in terms of linear matrix inequality(LMI). Finally, a numerical example is provided to illustrate the validity of the obtained results.
引文
[1]S.Leonid,Lyapunov Functionals and Stability of Stochastic Functional Differential Equations.New York:Springer,2013.
[2]X.Mao,and C.Yuan,Stochastic Differential Equations with Markovian Switching,London:Imperial College Press,2006.
[3]C.Gao,Z.Liu,and R.Xu,On exponential stabilization for a class of neutral-type systems with parameter uncertainties:An integral sliding mode approach,Appl.Math.Comput,219(23):11044–11055,2013.
[4]H.Chen,L.Wang,New result on exponential stability for neutral stochastic linear system with time-varying delay,Appl.Math.Comput,239:320–325,2014.
[5]Y.Kao,C.Wang,J.Xie,and H.R.Karimi,New delaydependent stability of Markovian jump neutral stochastic systems with general unknown transition rates,Int.J.Syst.Sci,47(11):1–11,2015.
[6]J.Xie,Y.Kao,C.Wang,and C.Gao,Delay-dependent robust stability of uncertain neutral-type Ito stoachstic systems with Markovian jumping parameter,Appl.Math.Comput,251:576–585,2015.
[7]Y.Kao,C.Wang,J.Xie,H.R.Karimi,and W.Li,H∞sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameter,Inform.Sci,314:200–211,2015.
[8]Y.Liu,Z.Wang,and X.Liu,Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays,Neurocomputing,94:46–53,2012.
[9]B.Song,J.H.Park,Z.Wu,and Y.Zhang,New resutls on delaydependent stability analysis for neutral stochastic delay systems,J.Franklin Inst,350(4):840–852,2013.
[10]Y.Kao,J.Guo,C.Wang,and X.Sun,Delay-dependent robust exponential staiblity of Markovian jumping reactiondiffusion Cohen-Grossberg neural networks with mixed delays,J.Franklin Inst,349(6):1972–1988,2012.
[11]Z.G.Wu,P.Shi,Z.Shu,H.Y.Su,and R.Q.Lu,Passivitybased asynchronous control for Markov jump systems,IEEE Trans.Autom.Control,DOI:10.1109/TAC.2016.2593742
[12]D.G.Luenberger,Observers for multi-variable systems,IEEE Trans.Autom.Control,11:190–197,1966.
[13]Z.Liu,C.Gao,Y.Kao,Robust H-infinity control for a class of neutral-type systems via sliding mode observer,Appl.Math.Comput,271:669–681,2015
[14]L.Wu,P.Shi,and H.Gao,State estimation and sliding mode control of Markovian jump singular systems,IEEE Trans.Autom.Control,55(5):1213–1219,2010.
[15]L.Wu,C.Wang,and Q.Zeng,Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems,J.Frankl.Inst,345(3):233–253,2008.
[16]Y.Zhu,L.Zhang,Z.Ning,Z.Zhu,W.Shammakh,and T.Hayat,H∞state estimation for discrete-time switching neural networks with persistent dwell-time switching,Neurocomputing,165(1):414–422,2015.
[17]L.Zhang,H∞estimation for discrete-time piecewise homogeneous Markov jump linear systems,Automatica,45(11):2570–2576,2009.
[18]Y.Liu,Y.Kao,H.R.Karimi,and Z.Gao,Input-to-state stability for discrete-time nonlinear switched singular systems,Inform.Sci,358-359:18-28,2016.
[19]H.Li,P.Shi,D.Yao,and L.Wu,Observer-based adaptive sliding mode control of nonlinear Markovian jump systems,Automatica,64(2):133–142,2016.
[20]Y.Kao,C.Wang,J.Xie,and H.R.Karimi,A sliding mode approach to H∞non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems,Automatica,52:218–226,2015.
[21]Y.Liu,C.Zhang,and C.Gao,Dynamic soft variable structure control of singular systems,Common Nonlinear Sci,17(8):3345-3352,2012.
[22]Y.Liu,Y.Kao,S.Gu,and H.R.Karimi,Soft variable structure controller design for singular systems,J.Frankl.Inst,352(4):1613-1626,2015.
[23]F.Zhong,H.Li,S.Zhong,State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems,Signal Processing,127:168–184,2016.
[24]B.Jiang,C.Gao,J.Xie,Passivity based sliding mode control of uncertain singular Markovian jump systems with timevarying delay and nonlinear perturbations,Appl.Math.Comput,271(11):187–200,2015.
[25]Y.Niu,and D.W.C.Ho,Robust observer design for It?o stochastic time-delay systems via sliding mode control,Syst.Control Lett,271:781–793,2006.
[26]D.Higham,An algorithmic introduction to mumerical simulation of stochastic differential equations,SIAM review,43:525–546,2001.
[2]X.Mao,and C.Yuan,Stochastic Differential Equations with Markovian Switching,London:Imperial College Press,2006.
[3]C.Gao,Z.Liu,and R.Xu,On exponential stabilization for a class of neutral-type systems with parameter uncertainties:An integral sliding mode approach,Appl.Math.Comput,219(23):11044–11055,2013.
[4]H.Chen,L.Wang,New result on exponential stability for neutral stochastic linear system with time-varying delay,Appl.Math.Comput,239:320–325,2014.
[5]Y.Kao,C.Wang,J.Xie,and H.R.Karimi,New delaydependent stability of Markovian jump neutral stochastic systems with general unknown transition rates,Int.J.Syst.Sci,47(11):1–11,2015.
[6]J.Xie,Y.Kao,C.Wang,and C.Gao,Delay-dependent robust stability of uncertain neutral-type Ito stoachstic systems with Markovian jumping parameter,Appl.Math.Comput,251:576–585,2015.
[7]Y.Kao,C.Wang,J.Xie,H.R.Karimi,and W.Li,H∞sliding mode control for uncertain neutral-type stochastic systems with Markovian jumping parameter,Inform.Sci,314:200–211,2015.
[8]Y.Liu,Z.Wang,and X.Liu,Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays,Neurocomputing,94:46–53,2012.
[9]B.Song,J.H.Park,Z.Wu,and Y.Zhang,New resutls on delaydependent stability analysis for neutral stochastic delay systems,J.Franklin Inst,350(4):840–852,2013.
[10]Y.Kao,J.Guo,C.Wang,and X.Sun,Delay-dependent robust exponential staiblity of Markovian jumping reactiondiffusion Cohen-Grossberg neural networks with mixed delays,J.Franklin Inst,349(6):1972–1988,2012.
[11]Z.G.Wu,P.Shi,Z.Shu,H.Y.Su,and R.Q.Lu,Passivitybased asynchronous control for Markov jump systems,IEEE Trans.Autom.Control,DOI:10.1109/TAC.2016.2593742
[12]D.G.Luenberger,Observers for multi-variable systems,IEEE Trans.Autom.Control,11:190–197,1966.
[13]Z.Liu,C.Gao,Y.Kao,Robust H-infinity control for a class of neutral-type systems via sliding mode observer,Appl.Math.Comput,271:669–681,2015
[14]L.Wu,P.Shi,and H.Gao,State estimation and sliding mode control of Markovian jump singular systems,IEEE Trans.Autom.Control,55(5):1213–1219,2010.
[15]L.Wu,C.Wang,and Q.Zeng,Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems,J.Frankl.Inst,345(3):233–253,2008.
[16]Y.Zhu,L.Zhang,Z.Ning,Z.Zhu,W.Shammakh,and T.Hayat,H∞state estimation for discrete-time switching neural networks with persistent dwell-time switching,Neurocomputing,165(1):414–422,2015.
[17]L.Zhang,H∞estimation for discrete-time piecewise homogeneous Markov jump linear systems,Automatica,45(11):2570–2576,2009.
[18]Y.Liu,Y.Kao,H.R.Karimi,and Z.Gao,Input-to-state stability for discrete-time nonlinear switched singular systems,Inform.Sci,358-359:18-28,2016.
[19]H.Li,P.Shi,D.Yao,and L.Wu,Observer-based adaptive sliding mode control of nonlinear Markovian jump systems,Automatica,64(2):133–142,2016.
[20]Y.Kao,C.Wang,J.Xie,and H.R.Karimi,A sliding mode approach to H∞non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems,Automatica,52:218–226,2015.
[21]Y.Liu,C.Zhang,and C.Gao,Dynamic soft variable structure control of singular systems,Common Nonlinear Sci,17(8):3345-3352,2012.
[22]Y.Liu,Y.Kao,S.Gu,and H.R.Karimi,Soft variable structure controller design for singular systems,J.Frankl.Inst,352(4):1613-1626,2015.
[23]F.Zhong,H.Li,S.Zhong,State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems,Signal Processing,127:168–184,2016.
[24]B.Jiang,C.Gao,J.Xie,Passivity based sliding mode control of uncertain singular Markovian jump systems with timevarying delay and nonlinear perturbations,Appl.Math.Comput,271(11):187–200,2015.
[25]Y.Niu,and D.W.C.Ho,Robust observer design for It?o stochastic time-delay systems via sliding mode control,Syst.Control Lett,271:781–793,2006.
[26]D.Higham,An algorithmic introduction to mumerical simulation of stochastic differential equations,SIAM review,43:525–546,2001.