Robust reliable control of uncertain 2D discrete switched systems with state delays

This paper is concerned with the problem of robust reliable control for a class of uncertain 2D discrete switched systems with state delays and actuator faults represented by a model of Roesser type. The parameter uncertainties are assumed to be norm-bounded. Firstly, based on the average dwell time approach, a delay-dependent sufficient condition for the exponential stability of discrete 2D switched systems with state delays is established in terms of linear matrix inequalities. Then, a reliable state feedback controller is designed to guarantee the exponential stability and reliability for the underlying systems. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

[1]  G. Marchesini,et al.  Stability analysis of 2-D systems , 1980 .

[2]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[3]  Wu-Sheng Lu,et al.  Comments on stability analysis for two-dimensional systems via a Lyapunov approach , 1985 .

[4]  Brian D. O. Anderson,et al.  Stability and the matrix Lyapunov equation for discrete 2-dimensional systems , 1986 .

[5]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[6]  Andreas Antoniou,et al.  Two-Dimensional Digital Filters , 2020 .

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

[8]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

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

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

[11]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  A. Michel,et al.  Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  Lihua Xie,et al.  H[∞] control and filtering of two-dimensional systems , 2002 .

[14]  Long Wang,et al.  Stabilization of switched linear systems with time-delay in detection of switching signal , 2005 .

[15]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

[16]  Yuan Gong Sun,et al.  Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays , 2006, Appl. Math. Comput..

[17]  Jun Zhao,et al.  GUARANTEED COST CONTROL FOR A CLASS OF UNCERTAIN SWITCHED DELAY SYSTEMS: AN AVERAGE DWELL-TIME METHOD , 2007, Cybern. Syst..

[18]  Guangming Xie,et al.  Delay-dependent robust stability and Hinfinity control for uncertain discrete-time switched systems with mode-dependent time delays , 2007, Appl. Math. Comput..

[19]  Man Liu,et al.  Reliable H∞ control for a class of switched nonlinear systems with actuator failures , 2007 .

[20]  Jun Zhao,et al.  ROBUST FAULT‐TOLERANT CONTROL FOR A CLASS OF SWITCHED NONLINEAR SYSTEMS IN LOWER TRIANGULAR FORM , 2007 .

[21]  Yijing Wang,et al.  Delay-dependent Robust H∞ Control for a Class of Switched Systems with Time Delay , 2008, 2008 IEEE International Symposium on Intelligent Control.

[22]  Yun Zou,et al.  Delay-dependent stability analysis for Two- Dimensional discrete systems with shift delays by the General Models , 2008, 2008 10th International Conference on Control, Automation, Robotics and Vision.

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

[24]  K. Hu,et al.  Improved robust H8 filtering for uncertain discrete-time switched systems , 2009 .

[25]  Georgi M. Dimirovski,et al.  Output feedback control for uncertain linear systems with faulty actuators based on a switching method , 2009 .

[26]  Jun Zhao,et al.  Tracking control for switched time-varying delays systems with stabilizable and unstabilizable subsystems , 2009 .

[27]  Abdellah Benzaouia,et al.  Stability conditions for discrete 2D switching systems, based on a multiple Lyapunov function , 2009, 2009 European Control Conference (ECC).

[28]  Li Xu,et al.  Delay-dependent robust stability and stabilisation of uncertain two-dimensional discrete systems with time-varying delays , 2010 .

[29]  Shyh-Feng Chen,et al.  Delay-dependent stability for 2-D systems with delays in the Roesser model , 2010, Proceedings of the 2010 American Control Conference.

[30]  Shyh-Feng Chen.  Stability analysis for 2-D systems with interval time-varying delays and saturation nonlinearities , 2010, Signal Process..

[31]  Shyh-Feng Chen,et al.  Delay-dependent stability for 2D systems with time-varying delay subject to state saturation in the Roesser model , 2010, Appl. Math. Comput..

[32]  Ahmed El Hajjaji,et al.  Stabilisation of discrete 2D time switching systems by state feedback control , 2011, Int. J. Syst. Sci..

[33]  Shuxia Ye,et al.  Stability analysis and stabilisation for a class of 2-D nonlinear discrete systems , 2011, Int. J. Syst. Sci..

[34]  Dan Zhang,et al.  Fault-Tolerant Control for Discrete-Time Switched Linear Systems with Time-Varying Delay and Actuator Saturation , 2011, Journal of Optimization Theory and Applications.

[35]  Zhengrong Xiang,et al.  Stability Analysis and Stabilization of Discrete-Time 2D Switched Systems , 2012, Circuits, Systems, and Signal Processing.