Delay-dependent stability of two-dimensional Markovian jump systems in the Roesser model with interval time-varying delays
详细信息 查看官网全文
- 英文论文题名：Delay-dependent stability of two-dimensional Markovian jump systems in the Roesser model with interval time-varying delays
- 论文作者：Jing Zhang ; Dan Peng ; Changchun Hua
- 英文论文作者：Jing Zhang ; Dan Peng ; Changchun Hua ; College of Science ; Yanshan University ; Institute of Electrical Engineering ; Yanshan University
- 年：2017
- 作者机构：College of Science,Yanshan University;Institute of Electrical Engineering,Yanshan University;
- 英文论文关键词：Two-dimensional Markovian jump systems(2D MJSs) ; Roesser model ; New finite-sum inequalities ; Interval timevarying delays ; Stochastic stability
- 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：O211.6
- 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：242k
- 原文格式：D
- 会议级别：全国
摘要
This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional Markovian jump systems(2D MJSs) described by the Roesser model. The systems under consideration are subject to interval time-varying and full known transition probabilities of the jumping process/Markov chain. First, new finite-sum inequalities are proposed in this paper. Then giving the Lyapunov-Krasovskii functional(LKF) with time-delay and differencing it via new finite-sum inequalities, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities(LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.
This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional Markovian jump systems(2D MJSs) described by the Roesser model. The systems under consideration are subject to interval time-varying and full known transition probabilities of the jumping process/Markov chain. First, new finite-sum inequalities are proposed in this paper. Then giving the Lyapunov-Krasovskii functional(LKF) with time-delay and differencing it via new finite-sum inequalities, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities(LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.
This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional Markovian jump systems(2D MJSs) described by the Roesser model. The systems under consideration are subject to interval time-varying and full known transition probabilities of the jumping process/Markov chain. First, new finite-sum inequalities are proposed in this paper. Then giving the Lyapunov-Krasovskii functional(LKF) with time-delay and differencing it via new finite-sum inequalities, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities(LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.
引文
[1]T.Kaczorek,Two-dimensional linear systems,Lecture Notes in Control and Information Sciences,Berlin:Springer,68,1985.
[2]H.Gao,X.Meng,T.Chen,New design of robust H∞filters for2-D systems,IEEE Signal Process.Lett,15:217-220,2008.
[3]D.Ding,X.Li,X.Yin,X.Xie,Further studies on relaxed stabilization conditions for discrete-time two-dimension TakagiSugeno fuzzy systems,Inform.Sci,189:143-154,2012.
[4]Z.Wu,R.Yang,P.Shi,X.Su,Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings,Automatica,59:206-215,2015.
[5]R.Sipahi,S.I.Niculescu,C.T.Abdallah,W.Michiels,K.Gu,Stability and stabilization of systems with time delay,IEEE Control Syst,31:38-65,2012.
[6]J.M.Xu,L.Yu,Delay-dependent H∞control for 2-D discrete state delay systems in the second FM model,Multidimens.Syst.Sign.Process,20(4):333-349,2009.
[7]S.F.Chen,Stability analysis for 2-D systems with interval time-varying delays and saturation nonlinearities,Signal Process,90(7):2265-2275,2010.
[8]D.Du,B.Qi,M.Fei,C.Peng,Multiple event-triggered H2/H∞filtering for hybrid wired-wireless networked systems with random network-induced delays,Inf.Sci,325:393-408,2015.
[9]A.Dey,H.Kar,LMI-based criterion for robust stability of2D discrete systems with interval time-varying delays employing quantisation/overflow nonlinearities,Multidim.Syst.Signal Process,25:473-492,2014.
[10]D.Peng,C.C.Hua,Improved approach to delay-dependent stability and stabilisation of two-dimensional discrete-time systems with interval time-varying delays,IET Control Theory Appl,9(12):1839-1845,2015.
[11]S.F.Chen,I.K.Fong,Robust filtering for 2-D state-delayed systems with NFT uncertainties,IEEE Trans.Signal Process,54(1):274-285,2006.
[12]D.Peng,X.P.Guan,H∞filtering of 2-D discrete state delayed systems,Multidim.Syst.Sign.Process,20(3):265-284,2009.
[13]Z.Wang,Y.Liu,X.Liu,Exponential stabilization of a class of stochastic system with markovian jump parameters and modedependent mixed time-delays,IEEE Trans.Autom.Control,55(7):1656-1662,2010.
[14]H.Gao,J.Lam,S.Xu,C.Wang,Stabilization and H∞control of two-dimensional Markovian jump systems,IMA J.Math.Control.Inf,21(4):377-392,2004.
[15]L.Wu,P.Shi,H.Gao,C.Wang,H∞filtering for 2D Markovian jump systems,Automatica,44(7):1849-1858,2008.
[16]R.Zhang,Y.Zhang,C.Hu,M.Q.Meng,Q.He,Delay-rangedependent filtering for two-dimensional Markovian jump systems with interval delays,IET Control Theory Appl,5(18):2191-2199,2011.
[17]Y.Wei,J.Qiu,H.R.Karimi,M.Wang,Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information,Inf.Sci,269:316-331,2014.
[18]L.V.Hien,H.Trinh,Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities,Inf.Sci,368:403-417,2016.
[19]P.G.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(1):235-238,2011.
[2]H.Gao,X.Meng,T.Chen,New design of robust H∞filters for2-D systems,IEEE Signal Process.Lett,15:217-220,2008.
[3]D.Ding,X.Li,X.Yin,X.Xie,Further studies on relaxed stabilization conditions for discrete-time two-dimension TakagiSugeno fuzzy systems,Inform.Sci,189:143-154,2012.
[4]Z.Wu,R.Yang,P.Shi,X.Su,Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings,Automatica,59:206-215,2015.
[5]R.Sipahi,S.I.Niculescu,C.T.Abdallah,W.Michiels,K.Gu,Stability and stabilization of systems with time delay,IEEE Control Syst,31:38-65,2012.
[6]J.M.Xu,L.Yu,Delay-dependent H∞control for 2-D discrete state delay systems in the second FM model,Multidimens.Syst.Sign.Process,20(4):333-349,2009.
[7]S.F.Chen,Stability analysis for 2-D systems with interval time-varying delays and saturation nonlinearities,Signal Process,90(7):2265-2275,2010.
[8]D.Du,B.Qi,M.Fei,C.Peng,Multiple event-triggered H2/H∞filtering for hybrid wired-wireless networked systems with random network-induced delays,Inf.Sci,325:393-408,2015.
[9]A.Dey,H.Kar,LMI-based criterion for robust stability of2D discrete systems with interval time-varying delays employing quantisation/overflow nonlinearities,Multidim.Syst.Signal Process,25:473-492,2014.
[10]D.Peng,C.C.Hua,Improved approach to delay-dependent stability and stabilisation of two-dimensional discrete-time systems with interval time-varying delays,IET Control Theory Appl,9(12):1839-1845,2015.
[11]S.F.Chen,I.K.Fong,Robust filtering for 2-D state-delayed systems with NFT uncertainties,IEEE Trans.Signal Process,54(1):274-285,2006.
[12]D.Peng,X.P.Guan,H∞filtering of 2-D discrete state delayed systems,Multidim.Syst.Sign.Process,20(3):265-284,2009.
[13]Z.Wang,Y.Liu,X.Liu,Exponential stabilization of a class of stochastic system with markovian jump parameters and modedependent mixed time-delays,IEEE Trans.Autom.Control,55(7):1656-1662,2010.
[14]H.Gao,J.Lam,S.Xu,C.Wang,Stabilization and H∞control of two-dimensional Markovian jump systems,IMA J.Math.Control.Inf,21(4):377-392,2004.
[15]L.Wu,P.Shi,H.Gao,C.Wang,H∞filtering for 2D Markovian jump systems,Automatica,44(7):1849-1858,2008.
[16]R.Zhang,Y.Zhang,C.Hu,M.Q.Meng,Q.He,Delay-rangedependent filtering for two-dimensional Markovian jump systems with interval delays,IET Control Theory Appl,5(18):2191-2199,2011.
[17]Y.Wei,J.Qiu,H.R.Karimi,M.Wang,Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information,Inf.Sci,269:316-331,2014.
[18]L.V.Hien,H.Trinh,Stability analysis of two-dimensional Markovian jump state-delayed systems in the Roesser model with uncertain transition probabilities,Inf.Sci,368:403-417,2016.
[19]P.G.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(1):235-238,2011.