Stability analysis of discrete-time randomly switched systems via an LMI approach
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- 英文论文题名：Stability analysis of discrete-time randomly switched systems via an LMI approach
- 论文作者：WANG Guoliang ; LI Zhiqiang
- 英文论文作者：WANG Guoliang ; LI Zhiqiang ; School of Information and Control Engineering ; Liaoning Shihua University
- 年：2017
- 作者机构：School of Information and Control Engineering,Liaoning Shihua University;
- 英文论文关键词：discrete-time randomly switched systems ; dwell time ; stochastic stability ; linear matrix inequality(LMI)
- 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：5
- 文件大小：210k
- 原文格式：D
- 会议级别：全国
摘要
This paper focuses on the stability problem of discrete-time randomly switched systems. Different from the traditional random switching signal, the realization of the switching needs to experience a fixed and random dwell time between each subsystems. Due to such a random switching signal included, the stochastic stability of the original system could be guaranteed by the established auxiliary system with state jumps. Particularly, the sufficient condition is established in term of LMI form.Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.
This paper focuses on the stability problem of discrete-time randomly switched systems. Different from the traditional random switching signal, the realization of the switching needs to experience a fixed and random dwell time between each subsystems. Due to such a random switching signal included, the stochastic stability of the original system could be guaranteed by the established auxiliary system with state jumps. Particularly, the sufficient condition is established in term of LMI form.Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.
This paper focuses on the stability problem of discrete-time randomly switched systems. Different from the traditional random switching signal, the realization of the switching needs to experience a fixed and random dwell time between each subsystems. Due to such a random switching signal included, the stochastic stability of the original system could be guaranteed by the established auxiliary system with state jumps. Particularly, the sufficient condition is established in term of LMI form.Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.
引文
[1]X.D.Zhao,L.X.Zhang,P.Shi and M.Liu,“Stability of switched positive linear systems with average dwell time switching,”Automatica,vol.48,no.6,pp.1132-1137,2012.
[2]Y.F.Su and J.Huang,“Stability of a class of linear switching systems with applications to two consensus problems,”IEEETransactions on Automatic Control,vol.57,no.6,pp.1420-1430,2012.
[3]Z.J.Wu,M.Y.Cui,P.Shi and H.R.Karimi,“Stability of stochastic nonlinear systems with state-dependent switching,”IEEE Transactions on Automatic Control,vol.58,no.8,pp.1904-1918,2013.
[4]J.L.Xiong,J.Lams,Z.Shu and X.R.Mao,“Stability analysis of continuous-time switched systems with a random switching signal,”IEEE Transactions on Automatic Control,vol.59,no.1,pp.180-186,2014.
[5]Y.Kang,D.H.Zhai,G.P.Liu and Y.B.Zhao,“On input-tostate stability of switched stochastic nonlinear systems under extended asynchronous switching,”IEEE Transactions on Cybernetics,vol.46,no.5,pp.1092-1105,2016.
[6]M.Philippe,R.Essick,G.E.Dullerud and R.M.Jungers,“Stability of discrete-time switching systems with constrained switching sequences,”Automatica,vol.72,pp.242-250,2016.
[7]V.N.Phat and K.Ratchagit,“Stability and stabilization of switched linear discrete-time systems with interval timevarying delay,”Nonlinear Analysis:Hybrid Systems,vol.5,no.4,pp.605-612,2011.
[8]H.Liu,Y.Shen and X.D.Zhao,“Finite-time stabilization and boundedness of switched linear system under statedependent switching,”Journal of the Franklin Institute,vol.350,no.3,pp.541-555,2013.
[9]X.D.Zhao,S.Yin,H.Y.Li and B.Niu,“Switching stabilization for a class of slowly switched systems,”IEEE Transactions on Automatic Control,vol.60,no.1,pp.221-226,2015.
[10]W.Ren and J.L.Xiong,“Stability and stabilization of switched stochastic systems under asynchronous switching,”Systems and Control Letters,vol.97,pp.184-192,2016.
[11]L.Liu,Q.Zhou,H.J.Liang and L.J.Wang,“Stability and stabilization of nonlinear switched systems under average dwell time,”Applied Mathematics and Computation,vol.298,pp.77-94,2017.
[12]X.D.Zhao,X.L.Zheng,B.Niu and L.Liu,“Adaptive tracking control for a class of uncertain switched nonlinear systems,”Automatica,vol.52,pp.185-191,2015.
[13]L.J.Long,Z.Wang and J.Zhao,“Switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems,”Automatica,vol.54,pp.217-228,2015.
[14]H.Wang,Y.J.Liu and S.C.Tong,“Adaptive control of a class of switched nonlinear discrete-time systems with unknown parameter,”Neurocomputing,vol.214,pp.1-6,2016.
[15]X.D.Zhao,X.W.Liu,S.Yin and H.Y.Li,“Improved results on stability of continuous-time switched positive linear systems,”Automatica,vol.50,no.2,pp.614-621,2014.
[16]X.J.Su,P.Shi,L.G.Wu and Y.D.Song,“Fault detection filtering for nonlinear switched stochastic systems,”IEEETransactions on Automatic Control,vol.61,no.5,pp.1310-1315,2015.
[17]I.Ghous and Z.R.Xiang,“H∞control of a class of 2-D continuous switched delayed systems via state-dependent switching,”Internation Journal of Systems Science,vol.47,no.2,pp.300-313,2016.
[18]L.Hetel and E.Fridman,“Robust sampled-data control of switched affine systems,”IEEE Transactions on Automatic Control,vol.58,no.11,pp.2922-2928,2013.
[19]K.Mathiyalagan,J.H.Park and R.Sakthivel,“Observerbased dissipative control for networked control systems:a switched system approach,”Complexity,vol.21,no.2,pp.297-308,2015.
[20]G.D.Zong,R.H.Wang,W.X.Zheng and L.L.Hou,“Finite-time H∞control for discrete-time switched nonlinear systems with time delay,”International Journal of Robust and Nonlinear Control,vol.25,no.6,pp.914-936,2015.
[21]H.Yang,B.Jiang,G.Tao and D.H.Zhou,“Robust stability of switched nonlinear system with switching uncertainties,”IEEE Transactions on Automatic Control,vol.61,no.9,pp.2531-2537,2016.
[22]W.B.Zhang,Y.Tang,Q.Y.Miao and W.Du,“Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects,”IEEE Transactions on Neural Networks and Learing Systems,vol.24,no.8,pp.1316-1326,2013.
[23]A.Abdurahman,H.J.Jiang and Z.D.Teng,“Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control,”Journal of Franklin Institute,vol.353,no.13,pp.2859-2880,2016.
[24]X.Y.Liu,J.D.Cao,W.W.Yu and Q.Song,“Nonsmooth finite-time synchronization of switched coupled neural networks,”IEEE Transactions on Cybernetics,vol.46,no.10,pp.2360-2371,2016.
[25]R.Wang,Z.G.Wu and P.Shi,“Dynamic output feedback control for a class of switched delay systems under asynchronous switching,”Information Sciences,vol.225,pp.72-80,2013.
[26]D.Zhai,A.Y.Lu,J.H.Li and Q.L.Zhang,“State and dynamic output feedback control of switched linear systems via a mixed time and state-dependent switching,”Nonlinear Analysis:Hybrid Systems,vol.22,pp.228-248,2016.
[27]H.Y.Li,Y.N.Pan,P.Shi and Y.Shi,“Switched fuzzy output feedback control and its application to a mass-springdamping system,”IEEE Transactions on Fuzzy Systems,vol.24,no.6,pp.1259-1269,2016.
[28]G.L.Wang and Q.L.Zhang,“Robust control of uncertain singular stochastic systems with markovian switching via proportional-derivative state feedback,”IET Control Theory and Applications,vol.6,no.8,pp.1089-1096,2012.
[29]G.D.Zong,D.Yang,L.L.Hou and Q.Z.Wang,“Robust finite-time H∞control for markovian jump systems with partially known transition probabilities,”Journal of the Franklin Institute,vol.350,no.6,pp.1562-1578,2013.
[30]B.Chen,Y.G.Niu and Y.Y.Zou,“Adaptive sliding mode control for stochastic markovian jumping systems with actuator degradation,”Automatica,vol.49,no.6,pp.1748-1754,2013.
[31]S.L.Kong and Z.S.Zhang,“Optimal control of stochastic system with markovian jumping and multiplicative noises,”IEEE Transactions on Automatic Control,vol.38,no.7,pp.1113-1118,2013.
[32]H.Y.Li,H.J.Gao,P.Shi and X.D.Zhao,“Fault-tolerant control of markovian jump stochastic systems via the augmented sliding mode observer approach,”Automatica,vol.50,no.7,pp.1825-1834,2014.
[33]G.L.Wang,Q.L.Zhang and C.Y.Yang,“Stabilization of singular markovian jump systems with time-varying switchings,”Information Science,vol.297,pp.254-270,2015.
[34]N.K.Kwon,B.Y.Park,P.G.Park and I.S.Park,“Improved H∞state-feedback control for continuous-time markovian jump fuzzy systems with incomplete knowledge of transition probabilities,”Journal of the Franklin Institute,vol.353,no.15,pp.3985-3998,2016.
[35]G.L.Wang,Q.L.Zhang,C.Y.Yang and C.L.Su,“Stability and stabilization of continuous-time stochastic markovian jump systems with random switching signals,”Journal of the Franklin Institute,vol.353,no.6,pp.1339-1357,2016.
[36]J.W.Wen,S.K.Nguang,P.Shi and L.Peng,“Finite-time stabilization of markovian jump delay systems-a switching control approach,”International Journal of Robust and Nonlinear Control,vol.27,no.2,pp.298-318,2017.
[2]Y.F.Su and J.Huang,“Stability of a class of linear switching systems with applications to two consensus problems,”IEEETransactions on Automatic Control,vol.57,no.6,pp.1420-1430,2012.
[3]Z.J.Wu,M.Y.Cui,P.Shi and H.R.Karimi,“Stability of stochastic nonlinear systems with state-dependent switching,”IEEE Transactions on Automatic Control,vol.58,no.8,pp.1904-1918,2013.
[4]J.L.Xiong,J.Lams,Z.Shu and X.R.Mao,“Stability analysis of continuous-time switched systems with a random switching signal,”IEEE Transactions on Automatic Control,vol.59,no.1,pp.180-186,2014.
[5]Y.Kang,D.H.Zhai,G.P.Liu and Y.B.Zhao,“On input-tostate stability of switched stochastic nonlinear systems under extended asynchronous switching,”IEEE Transactions on Cybernetics,vol.46,no.5,pp.1092-1105,2016.
[6]M.Philippe,R.Essick,G.E.Dullerud and R.M.Jungers,“Stability of discrete-time switching systems with constrained switching sequences,”Automatica,vol.72,pp.242-250,2016.
[7]V.N.Phat and K.Ratchagit,“Stability and stabilization of switched linear discrete-time systems with interval timevarying delay,”Nonlinear Analysis:Hybrid Systems,vol.5,no.4,pp.605-612,2011.
[8]H.Liu,Y.Shen and X.D.Zhao,“Finite-time stabilization and boundedness of switched linear system under statedependent switching,”Journal of the Franklin Institute,vol.350,no.3,pp.541-555,2013.
[9]X.D.Zhao,S.Yin,H.Y.Li and B.Niu,“Switching stabilization for a class of slowly switched systems,”IEEE Transactions on Automatic Control,vol.60,no.1,pp.221-226,2015.
[10]W.Ren and J.L.Xiong,“Stability and stabilization of switched stochastic systems under asynchronous switching,”Systems and Control Letters,vol.97,pp.184-192,2016.
[11]L.Liu,Q.Zhou,H.J.Liang and L.J.Wang,“Stability and stabilization of nonlinear switched systems under average dwell time,”Applied Mathematics and Computation,vol.298,pp.77-94,2017.
[12]X.D.Zhao,X.L.Zheng,B.Niu and L.Liu,“Adaptive tracking control for a class of uncertain switched nonlinear systems,”Automatica,vol.52,pp.185-191,2015.
[13]L.J.Long,Z.Wang and J.Zhao,“Switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems,”Automatica,vol.54,pp.217-228,2015.
[14]H.Wang,Y.J.Liu and S.C.Tong,“Adaptive control of a class of switched nonlinear discrete-time systems with unknown parameter,”Neurocomputing,vol.214,pp.1-6,2016.
[15]X.D.Zhao,X.W.Liu,S.Yin and H.Y.Li,“Improved results on stability of continuous-time switched positive linear systems,”Automatica,vol.50,no.2,pp.614-621,2014.
[16]X.J.Su,P.Shi,L.G.Wu and Y.D.Song,“Fault detection filtering for nonlinear switched stochastic systems,”IEEETransactions on Automatic Control,vol.61,no.5,pp.1310-1315,2015.
[17]I.Ghous and Z.R.Xiang,“H∞control of a class of 2-D continuous switched delayed systems via state-dependent switching,”Internation Journal of Systems Science,vol.47,no.2,pp.300-313,2016.
[18]L.Hetel and E.Fridman,“Robust sampled-data control of switched affine systems,”IEEE Transactions on Automatic Control,vol.58,no.11,pp.2922-2928,2013.
[19]K.Mathiyalagan,J.H.Park and R.Sakthivel,“Observerbased dissipative control for networked control systems:a switched system approach,”Complexity,vol.21,no.2,pp.297-308,2015.
[20]G.D.Zong,R.H.Wang,W.X.Zheng and L.L.Hou,“Finite-time H∞control for discrete-time switched nonlinear systems with time delay,”International Journal of Robust and Nonlinear Control,vol.25,no.6,pp.914-936,2015.
[21]H.Yang,B.Jiang,G.Tao and D.H.Zhou,“Robust stability of switched nonlinear system with switching uncertainties,”IEEE Transactions on Automatic Control,vol.61,no.9,pp.2531-2537,2016.
[22]W.B.Zhang,Y.Tang,Q.Y.Miao and W.Du,“Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects,”IEEE Transactions on Neural Networks and Learing Systems,vol.24,no.8,pp.1316-1326,2013.
[23]A.Abdurahman,H.J.Jiang and Z.D.Teng,“Exponential lag synchronization for memristor-based neural networks with mixed time delays via hybrid switching control,”Journal of Franklin Institute,vol.353,no.13,pp.2859-2880,2016.
[24]X.Y.Liu,J.D.Cao,W.W.Yu and Q.Song,“Nonsmooth finite-time synchronization of switched coupled neural networks,”IEEE Transactions on Cybernetics,vol.46,no.10,pp.2360-2371,2016.
[25]R.Wang,Z.G.Wu and P.Shi,“Dynamic output feedback control for a class of switched delay systems under asynchronous switching,”Information Sciences,vol.225,pp.72-80,2013.
[26]D.Zhai,A.Y.Lu,J.H.Li and Q.L.Zhang,“State and dynamic output feedback control of switched linear systems via a mixed time and state-dependent switching,”Nonlinear Analysis:Hybrid Systems,vol.22,pp.228-248,2016.
[27]H.Y.Li,Y.N.Pan,P.Shi and Y.Shi,“Switched fuzzy output feedback control and its application to a mass-springdamping system,”IEEE Transactions on Fuzzy Systems,vol.24,no.6,pp.1259-1269,2016.
[28]G.L.Wang and Q.L.Zhang,“Robust control of uncertain singular stochastic systems with markovian switching via proportional-derivative state feedback,”IET Control Theory and Applications,vol.6,no.8,pp.1089-1096,2012.
[29]G.D.Zong,D.Yang,L.L.Hou and Q.Z.Wang,“Robust finite-time H∞control for markovian jump systems with partially known transition probabilities,”Journal of the Franklin Institute,vol.350,no.6,pp.1562-1578,2013.
[30]B.Chen,Y.G.Niu and Y.Y.Zou,“Adaptive sliding mode control for stochastic markovian jumping systems with actuator degradation,”Automatica,vol.49,no.6,pp.1748-1754,2013.
[31]S.L.Kong and Z.S.Zhang,“Optimal control of stochastic system with markovian jumping and multiplicative noises,”IEEE Transactions on Automatic Control,vol.38,no.7,pp.1113-1118,2013.
[32]H.Y.Li,H.J.Gao,P.Shi and X.D.Zhao,“Fault-tolerant control of markovian jump stochastic systems via the augmented sliding mode observer approach,”Automatica,vol.50,no.7,pp.1825-1834,2014.
[33]G.L.Wang,Q.L.Zhang and C.Y.Yang,“Stabilization of singular markovian jump systems with time-varying switchings,”Information Science,vol.297,pp.254-270,2015.
[34]N.K.Kwon,B.Y.Park,P.G.Park and I.S.Park,“Improved H∞state-feedback control for continuous-time markovian jump fuzzy systems with incomplete knowledge of transition probabilities,”Journal of the Franklin Institute,vol.353,no.15,pp.3985-3998,2016.
[35]G.L.Wang,Q.L.Zhang,C.Y.Yang and C.L.Su,“Stability and stabilization of continuous-time stochastic markovian jump systems with random switching signals,”Journal of the Franklin Institute,vol.353,no.6,pp.1339-1357,2016.
[36]J.W.Wen,S.K.Nguang,P.Shi and L.Peng,“Finite-time stabilization of markovian jump delay systems-a switching control approach,”International Journal of Robust and Nonlinear Control,vol.27,no.2,pp.298-318,2017.