Finite-Time Stability for Markovian Jump Nonlinear Systems with Random Delays
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- 英文论文题名：Finite-Time Stability for Markovian Jump Nonlinear Systems with Random Delays
- 论文作者：CHEN Haiyang ; LIU Meiqin ; ZHANG Senlin
- 英文论文作者：CHEN Haiyang ; LIU Meiqin ; ZHANG Senlin ; State Key Laboratory of Industrial Control Technology ; Zhejiang University ; College of Electrical Engineering ; Zhejiang University
- 年：2017
- 作者机构：State Key Laboratory of Industrial Control Technology,Zhejiang University;College of Electrical Engineering,Zhejiang University;
- 英文论文关键词：Markovian jump nonlinear systems ; stochastic control ; random delays ; finite-time stability ; Bernoulli distribution
- 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：7
- 文件大小：249k
- 原文格式：D
- 会议级别：全国
摘要
This paper investigates the stochastic finite-time stability(SFTS) problem for a class of Markovian jump nonlinear systems with time delays. The nonlinear terms are assumed to satisfy the Lipschitz conditions, and the time delays are modelled by mutually independent stochastic variables subject to Bernoulli distributions. The aim of our work is to design a set of linear feedback controllers such that the addressed system is SFTS in the presence of Markov jumps, random delays, and nonlinearity.In our work, first the SFTS performances are analyzed by virtue of Lyapunov functional and stochastic control strategy. Then according to these analyses, new criterion are given in terms of linear matrix inequalities(LMIs) in order to design the feedback controller. In addition, a reasonable strategy is proposed to reduce the resource consumption of controller design. And the effect of random delays on control performances is also discussed. Finally, an illustrative example is provided to validate the proposed method.
This paper investigates the stochastic finite-time stability(SFTS) problem for a class of Markovian jump nonlinear systems with time delays. The nonlinear terms are assumed to satisfy the Lipschitz conditions, and the time delays are modelled by mutually independent stochastic variables subject to Bernoulli distributions. The aim of our work is to design a set of linear feedback controllers such that the addressed system is SFTS in the presence of Markov jumps, random delays, and nonlinearity.In our work, first the SFTS performances are analyzed by virtue of Lyapunov functional and stochastic control strategy. Then according to these analyses, new criterion are given in terms of linear matrix inequalities(LMIs) in order to design the feedback controller. In addition, a reasonable strategy is proposed to reduce the resource consumption of controller design. And the effect of random delays on control performances is also discussed. Finally, an illustrative example is provided to validate the proposed method.
This paper investigates the stochastic finite-time stability(SFTS) problem for a class of Markovian jump nonlinear systems with time delays. The nonlinear terms are assumed to satisfy the Lipschitz conditions, and the time delays are modelled by mutually independent stochastic variables subject to Bernoulli distributions. The aim of our work is to design a set of linear feedback controllers such that the addressed system is SFTS in the presence of Markov jumps, random delays, and nonlinearity.In our work, first the SFTS performances are analyzed by virtue of Lyapunov functional and stochastic control strategy. Then according to these analyses, new criterion are given in terms of linear matrix inequalities(LMIs) in order to design the feedback controller. In addition, a reasonable strategy is proposed to reduce the resource consumption of controller design. And the effect of random delays on control performances is also discussed. Finally, an illustrative example is provided to validate the proposed method.
引文
[1]Y.Chen,Q.Liu,R.Lu,and A.Xue.Finite-time control of switched stochastic delayed systems.Neurocompt.,191:374–379,2016.
[2]S.Shi,Z.Fei,and J.Li.Finite-time H∞control of switched systems with mode-dependent average dwell time.J.Frankl.Inf.,353(1):221-234,2016.
[3]O.Costa,M.Fragoso,and R.Marques.Discrete-Time Markov Jump Linear Systems(Probability and Its Applications).Springer,Berlin,Germany,2005.
[4]N.Thanh,P.Niamsup,and V.Phat.Finite-time stability of singular nonlinear switched time-delay systems:A singular value decomposition approach.J.Frankl.Inf.,354(8):3502-3518,2017.
[5]H.Chen,M.Liu,and S.Zhang.Robust H∞input-output finite time boundedness of delayed nonlinear systems:Analysis and controller design.Proc.of the 35th Chinese Control Conference(CCC’15),Hangzhou,China,2015:2943–2948.
[6]F.Amato,M.Ariola and P.Dorato.Finite-time control of linear systems subject to parametric uncertainties and disturbances.IEEE Trans.Autom.Control,37(9):1459–1463,2001.
[7]H.Wang,P.Shi,and R.Agarwal.Network-based eventtriggered filtering for Markovian jump systems.Int.J.Control,89(6):1096–1110,2016.
[8]X.Li,J.Lam,H.Gao,and P.Li.Improved results on H∞model reduction for Markovian jump systems with partly known transition probabilities.Syst.Control Lett.,70:109–117,2014
[9]H.Chen,M.Liu and S.Zhang.Robust H∞finite-time control for discrete Markovian jump systems with disturbances of probabilistic distributions.Entropy,17(1):346–367,2015.
[10]A.Ray.Output feedback control under randomly varying distributed delays.J.Guid.Control Dynam.,17(4):701-711,1994.
[11]R.Rakkiyappan,R.Sasirekha,S.Lakshmanan,and C.Lim.Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control.J.Frankl.Inf.,353(16):4300-4329,2016.
[12]H.Yan,F.Qian,F.Yang,and H.Shi.H∞filtering for nonlinear networked systems with randomly occurring distributed delays,missing measurements and sensor saturation.Inform.Sciences,370–371:772–782,2015.
[13]S.Zhang,Z.Wang,D.Ding,and H.Shu.H∞outputfeedback control with randomly occurring distributed delays and nonlinearities subject to sensor saturations and channel fadings.J.Frankl.Inf.,351(8):4124–4141,2014.
[14]S.P.Boyed,L.E.Ghaoui,E.Feron and V.Balakrishnan.Linear Matrix Inequalities in System and Control Theory.Philadelphia,PA:SIAM,1994.
[2]S.Shi,Z.Fei,and J.Li.Finite-time H∞control of switched systems with mode-dependent average dwell time.J.Frankl.Inf.,353(1):221-234,2016.
[3]O.Costa,M.Fragoso,and R.Marques.Discrete-Time Markov Jump Linear Systems(Probability and Its Applications).Springer,Berlin,Germany,2005.
[4]N.Thanh,P.Niamsup,and V.Phat.Finite-time stability of singular nonlinear switched time-delay systems:A singular value decomposition approach.J.Frankl.Inf.,354(8):3502-3518,2017.
[5]H.Chen,M.Liu,and S.Zhang.Robust H∞input-output finite time boundedness of delayed nonlinear systems:Analysis and controller design.Proc.of the 35th Chinese Control Conference(CCC’15),Hangzhou,China,2015:2943–2948.
[6]F.Amato,M.Ariola and P.Dorato.Finite-time control of linear systems subject to parametric uncertainties and disturbances.IEEE Trans.Autom.Control,37(9):1459–1463,2001.
[7]H.Wang,P.Shi,and R.Agarwal.Network-based eventtriggered filtering for Markovian jump systems.Int.J.Control,89(6):1096–1110,2016.
[8]X.Li,J.Lam,H.Gao,and P.Li.Improved results on H∞model reduction for Markovian jump systems with partly known transition probabilities.Syst.Control Lett.,70:109–117,2014
[9]H.Chen,M.Liu and S.Zhang.Robust H∞finite-time control for discrete Markovian jump systems with disturbances of probabilistic distributions.Entropy,17(1):346–367,2015.
[10]A.Ray.Output feedback control under randomly varying distributed delays.J.Guid.Control Dynam.,17(4):701-711,1994.
[11]R.Rakkiyappan,R.Sasirekha,S.Lakshmanan,and C.Lim.Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control.J.Frankl.Inf.,353(16):4300-4329,2016.
[12]H.Yan,F.Qian,F.Yang,and H.Shi.H∞filtering for nonlinear networked systems with randomly occurring distributed delays,missing measurements and sensor saturation.Inform.Sciences,370–371:772–782,2015.
[13]S.Zhang,Z.Wang,D.Ding,and H.Shu.H∞outputfeedback control with randomly occurring distributed delays and nonlinearities subject to sensor saturations and channel fadings.J.Frankl.Inf.,351(8):4124–4141,2014.
[14]S.P.Boyed,L.E.Ghaoui,E.Feron and V.Balakrishnan.Linear Matrix Inequalities in System and Control Theory.Philadelphia,PA:SIAM,1994.