H_∞ Control of Continuous-Time Descriptor Semi-Markov Jump Systems Subject to Actuator Saturation
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- 英文论文题名：H_∞ Control of Continuous-Time Descriptor Semi-Markov Jump Systems Subject to Actuator Saturation
- 论文作者：Yi Zhou ; Shuping Ma ; Zhumahan Kulan
- 英文论文作者：Yi Zhou ; Shuping Ma ; Zhumahan Kulan ; School of Mathematics ; Shandong University ; Department of Mathematics ; Changji College
- 年：2017
- 作者机构：School of Mathematics,Shandong University;Department of Mathematics,Changji College;
- 英文论文关键词：Descriptor semi-Markov jump systems ; Actuator saturation ; Stochastically admissible with γ-disturbance attenuation ; H∞ performance ; Optimization problem
- 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：297k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the H_∞ control problem of the continuous-time descriptor semi-Markov jump systems(S-MJSs) with actuator saturation is discussed. First, a sufficient condition is obtained to guarantee that this kind of systems are stochastically admissible with γ-disturbance attenuation by applying infinitesimal generator for stochastic Lyapunov function. Then, based on the lower and upper bounds of the time-varying transition probability, and the singular value decomposition approach, another sufficient condition is given to guarantee the descriptor S-MJSs being stochastically admissible with γ-disturbance attenuation.Next, a strict linear matrix inequalities(LMIs) optimization problem is developed to solve the H_∞ control problem and design the H_∞ state feedback controller. Last, a numerical example is given to illustrate the effectiveness of the proposed methods.
In this paper, the H_∞ control problem of the continuous-time descriptor semi-Markov jump systems(S-MJSs) with actuator saturation is discussed. First, a sufficient condition is obtained to guarantee that this kind of systems are stochastically admissible with γ-disturbance attenuation by applying infinitesimal generator for stochastic Lyapunov function. Then, based on the lower and upper bounds of the time-varying transition probability, and the singular value decomposition approach, another sufficient condition is given to guarantee the descriptor S-MJSs being stochastically admissible with γ-disturbance attenuation.Next, a strict linear matrix inequalities(LMIs) optimization problem is developed to solve the H_∞ control problem and design the H_∞ state feedback controller. Last, a numerical example is given to illustrate the effectiveness of the proposed methods.
In this paper, the H_∞ control problem of the continuous-time descriptor semi-Markov jump systems(S-MJSs) with actuator saturation is discussed. First, a sufficient condition is obtained to guarantee that this kind of systems are stochastically admissible with γ-disturbance attenuation by applying infinitesimal generator for stochastic Lyapunov function. Then, based on the lower and upper bounds of the time-varying transition probability, and the singular value decomposition approach, another sufficient condition is given to guarantee the descriptor S-MJSs being stochastically admissible with γ-disturbance attenuation.Next, a strict linear matrix inequalities(LMIs) optimization problem is developed to solve the H_∞ control problem and design the H_∞ state feedback controller. Last, a numerical example is given to illustrate the effectiveness of the proposed methods.
引文
[1]L.Dai,Singular Control Systems,Lecture Notes in Control and Information Sciences.New York:Springer-Verlag,1989.
[2]S.Xu and J.Lam,Robust Control and Filtering of Singular Systems.Berlin:Springer-Verlag,2006.
[3]S.Ma,C.Zhang and X.Liu,Robust Sstability for discretetime uncertain Markovian jump singular systems,Journal of Control Theory and Applications,6(2):133–140,2008.
[4]L.Zhang and E.K.Boukas,Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities,Automatica,45(2):463–468,2009.
[5]O.L,V.Costa,M.D.Fragoso and M.G.Todorow,Continuoustime Markov Jump Linear System.London:Springer-Verlag,2013.
[6]Y.Xia,E.K.Boukas,P.Shi and J.Zhang,Stability and stabilization of continuous-time singular hydrid systems,Automatica,45(6):1504–1509,2009.
[7]S.Song,S.Ma and C.Zhang,Stability and robust stabilization for a class of non-linear uncertain discrete-time singular Markov jump systems,IET Control Theory and Applications,6(16):2518–2527,2012.
[8]H.Shen,J.H.Park,L.Zhang and Z.Wu,Robust extended dissipative control for sampled-data Markov jump systems,International Journal of Control,87(8):1549–1564,2014.
[9]Z.Hou,J.Luo and P.Shi,Stochastic stability of linear systems with semi-Markovian jump parameters,ANZIAM J,46(3):331–340,2005.
[10]J.Huang and Y.Shi,Stochastic stability of semi-Markovian jump linear systems:an LMI approach,Proceeding of 50th IEEE Conference on Decision and Control and European Control Conference,4668–4673,2011.
[11]J.Wang,S.Ma and C.Zhang,Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems,Applied Mathematics and Computation,279:90–102,2016.
[12]L.Zhang,Y.Leng and P.Colaneri,Stability and stabilization of discrete-time semi-Markov jump systems via semi-Markov kernel approach,IEEE Trans.Autom.Control,61(2):503–508,2016.
[13]J.Wang,S.Ma and Z.Kulan,Finite-time H∞control of nonlinear continuous-time descriptor semi-Markov jump systems,Proceeding of the 35th Chinese Control Coference,1690–1695,2016.
[14]T.Hu,Z.Lin and B.M.Chen,Analysis and design for discrete-time linear systems subject to actuator saturation,Systems Control Letters,45(2):97–112,2002.
[15]Y.Cao and Z.Lin,Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function,Automatica,39(7):1235–1241,2003.
[16]Z.Lin and Lv.Liang,Set invariance conditions for singular linear systems subject to actuator saturation,IEEE Trans.Autom.Control,52(12),2351–2355,2007.
[17]S.Ma and E.K.Boukas,Stability and H∞control for discrete-time singular systems subject to sctuator saturation,2009 American Control Conference,Hyatt Regency Riverfront,St.Louis,MO,USA,1244–1249,2009.
[18]J.R.Liang,H.L.Choi and J.T.Lim,On stability of singular systems with saturating actuators,IEICE Trans.Fundament.Electron.,Commun.Comp.Sci.,E86-A(10):2700–2703,2003.
[19]H.Liu,F.Sun and E.K.Boukas,Robust control of uncertain discrete-time Markovian jump systems with actuator saturation,International Journal of Control,79(7):805–812,2006.
[20]Z.Zuo,Y.Cui,Y.Wang and G.Zhang,Non-fragile control of uncertain Markovian jumping linear systems subject to actuator saturation,2009 Chinese Control and Decision conf.,2210–2215,2009.
[21]S.Ma and C.Zhang,H∞control for discrete-time singular Markov jump systems subject to actuator saturation,Journal of the Franklin Institute,349(3):1011–1029,2012.
[22]Y.Ma,M.Chen and Q.Zhang,Non-fragile static output feedback control for singular T-S fuzzy delay-dependent systems subject to Markovian jump and actuator saturation,Journal of the Franklin Institute,353(11):2373–2397,2016.
[23]W.Guan and F.Liu,Finite-time dissipative control for singular T-S fuzzy Markovian jump systems under actuator saturation with partly unknown transition rates,Neurocomputing,207:60–70,2016.
[2]S.Xu and J.Lam,Robust Control and Filtering of Singular Systems.Berlin:Springer-Verlag,2006.
[3]S.Ma,C.Zhang and X.Liu,Robust Sstability for discretetime uncertain Markovian jump singular systems,Journal of Control Theory and Applications,6(2):133–140,2008.
[4]L.Zhang and E.K.Boukas,Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities,Automatica,45(2):463–468,2009.
[5]O.L,V.Costa,M.D.Fragoso and M.G.Todorow,Continuoustime Markov Jump Linear System.London:Springer-Verlag,2013.
[6]Y.Xia,E.K.Boukas,P.Shi and J.Zhang,Stability and stabilization of continuous-time singular hydrid systems,Automatica,45(6):1504–1509,2009.
[7]S.Song,S.Ma and C.Zhang,Stability and robust stabilization for a class of non-linear uncertain discrete-time singular Markov jump systems,IET Control Theory and Applications,6(16):2518–2527,2012.
[8]H.Shen,J.H.Park,L.Zhang and Z.Wu,Robust extended dissipative control for sampled-data Markov jump systems,International Journal of Control,87(8):1549–1564,2014.
[9]Z.Hou,J.Luo and P.Shi,Stochastic stability of linear systems with semi-Markovian jump parameters,ANZIAM J,46(3):331–340,2005.
[10]J.Huang and Y.Shi,Stochastic stability of semi-Markovian jump linear systems:an LMI approach,Proceeding of 50th IEEE Conference on Decision and Control and European Control Conference,4668–4673,2011.
[11]J.Wang,S.Ma and C.Zhang,Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems,Applied Mathematics and Computation,279:90–102,2016.
[12]L.Zhang,Y.Leng and P.Colaneri,Stability and stabilization of discrete-time semi-Markov jump systems via semi-Markov kernel approach,IEEE Trans.Autom.Control,61(2):503–508,2016.
[13]J.Wang,S.Ma and Z.Kulan,Finite-time H∞control of nonlinear continuous-time descriptor semi-Markov jump systems,Proceeding of the 35th Chinese Control Coference,1690–1695,2016.
[14]T.Hu,Z.Lin and B.M.Chen,Analysis and design for discrete-time linear systems subject to actuator saturation,Systems Control Letters,45(2):97–112,2002.
[15]Y.Cao and Z.Lin,Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function,Automatica,39(7):1235–1241,2003.
[16]Z.Lin and Lv.Liang,Set invariance conditions for singular linear systems subject to actuator saturation,IEEE Trans.Autom.Control,52(12),2351–2355,2007.
[17]S.Ma and E.K.Boukas,Stability and H∞control for discrete-time singular systems subject to sctuator saturation,2009 American Control Conference,Hyatt Regency Riverfront,St.Louis,MO,USA,1244–1249,2009.
[18]J.R.Liang,H.L.Choi and J.T.Lim,On stability of singular systems with saturating actuators,IEICE Trans.Fundament.Electron.,Commun.Comp.Sci.,E86-A(10):2700–2703,2003.
[19]H.Liu,F.Sun and E.K.Boukas,Robust control of uncertain discrete-time Markovian jump systems with actuator saturation,International Journal of Control,79(7):805–812,2006.
[20]Z.Zuo,Y.Cui,Y.Wang and G.Zhang,Non-fragile control of uncertain Markovian jumping linear systems subject to actuator saturation,2009 Chinese Control and Decision conf.,2210–2215,2009.
[21]S.Ma and C.Zhang,H∞control for discrete-time singular Markov jump systems subject to actuator saturation,Journal of the Franklin Institute,349(3):1011–1029,2012.
[22]Y.Ma,M.Chen and Q.Zhang,Non-fragile static output feedback control for singular T-S fuzzy delay-dependent systems subject to Markovian jump and actuator saturation,Journal of the Franklin Institute,353(11):2373–2397,2016.
[23]W.Guan and F.Liu,Finite-time dissipative control for singular T-S fuzzy Markovian jump systems under actuator saturation with partly unknown transition rates,Neurocomputing,207:60–70,2016.
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