Robust H∞ reliable control for uncertain switched systems with circular disk pole constraints

Abstract This paper addresses the issue of optimal robust H ∞ reliable control with circular disk pole constraints for switched systems with actuator faults and arbitrary switching rules. The design method of the state feedback controller is proposed, which guarantees that the robust H ∞ performance is minimum and the closed poles are located in a specified circular disk. The corresponding parameters of the controller are obtained by using the linear matrix inequalities (LMIs) optimization. Finally, a simulation example is provided to validate the effectiveness of the proposed approach.

[1]  Zhengrong Xiang,et al.  Robust L∞ reliable control for uncertain nonlinear switched systems with time delay , 2009, Appl. Math. Comput..

[2]  Bin Jiang,et al.  Fault tolerance analysis for stochastic systems using switching diffusion processes , 2009, Int. J. Control.

[3]  P. Shi,et al.  H∞ Output feedback control of fuzzy system models under sampled measurements , 2003 .

[4]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[5]  Sang Bong Kim,et al.  Pole assignment in a specified disk , 1987 .

[6]  Zhao Jun,et al.  H_∞ robust control of uncertain switched linear systems based on LMIs , 2005 .

[7]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[8]  Huijun Gao,et al.  Improved Hinfinite control of discrete-time fuzzy systems: a cone complementarity linearization approach , 2005, Inf. Sci..

[9]  Kevin Guelton,et al.  Robust pole placement controller design in LMI region for uncertain and disturbed switched systems , 2008 .

[10]  Jian Xiao,et al.  H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance , 2011, J. Frankl. Inst..

[11]  Marcel Staroswiecki,et al.  Supervisory fault tolerant control for a class of uncertain nonlinear systems , 2009, Autom..

[12]  Pascal Gahinet,et al.  H/sub /spl infin// design with pole placement constraints: an LMI approach , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[13]  Long-Yeu Chung,et al.  Switching signal design for exponential stability of discrete switched systems with interval time-varying delay , 2012, J. Frankl. Inst..

[14]  James Lam,et al.  Model simplification for switched hybrid systems , 2006, Syst. Control. Lett..

[15]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Long Wang,et al.  Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach , 2006 .

[17]  Choon Ki Ahn,et al.  L 2 - L ∞ filtering for time-delayed switched hopfield neural networks , 2011 .

[18]  Jun Zhao,et al.  Robust H∞ Control of Uncertain Switched Systems: a Sliding Mode Control Design , 2009 .

[19]  Peng Shi,et al.  Asynchronous H∞ filtering of discrete-time switched systems , 2012, Signal Process..

[20]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[21]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[22]  Jamal Daafouz,et al.  Dynamic output feedback Hinfinity control of switched linear systems , 2011, Autom..

[23]  Zhendong Sun A Note on Marginal Stability of Switched Systems , 2008, IEEE Trans. Autom. Control..

[24]  M. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[25]  Magdi S. Mahmoud,et al.  Guaranteed-cost reliable control with regional pole placement of a power system , 2011, J. Frankl. Inst..

[26]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[27]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[28]  连捷,et al.  不确定切换系统的鲁棒 H ∞ 控制:滑模控制设计 , 2009 .

[29]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[30]  Ahmed El Hajjaji,et al.  Observer-Based Robust $H_{\infty }$ Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay , 2010, IEEE Transactions on Fuzzy Systems.

[31]  S. B. Attia,et al.  STATIC SWITCHED OUTPUT FEEDBACK STABILIZATION FOR LINEAR DISCRETE-TIME SWITCHED SYSTEMS , 2012 .

[32]  Shu Yin,et al.  A switched system approach to H∞ control of networked control systems with time-varying delays , 2011, J. Frankl. Inst..

[33]  Peng Shi,et al.  H∞ model reduction for uncertain switched linear discrete-time systems , 2008, Autom..

[34]  Bin Jiang,et al.  Fault Tolerant Control Design for Hybrid Systems , 2010 .

[35]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..