Persistent bounded disturbance rejection for discrete-time delay systems

In this article, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov-function method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities to guarantee the desired ℓ1-performance. A robust state-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example.

[1]  El-Kébir Boukas,et al.  Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty , 2000, Int. J. Syst. Sci..

[2]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[3]  Kouider M'Sirdi,et al.  STABILIZATION OF LINEAR SYSTEMS VIA DELAYED STATE FEEDBACK CONTROLLER , 2008 .

[4]  E. Fridman,et al.  Delay-dependent stability and H ∞ control: Constant and time-varying delays , 2003 .

[5]  Ligang Wu,et al.  Sliding mode control of switched hybrid systems with time‐varying delay , 2008 .

[6]  Peng Shi,et al.  Delay-dependent robust ℋ∞ and ℒ2-ℒ∞ filtering for LPV systems with both discrete and distributed delays , 2006 .

[7]  Mathukumalli Vidyasagar,et al.  Further results on the optimal rejection of persistent bounded disturbances , 1991 .

[8]  Yuanqing Xia,et al.  Active disturbance rejection control for uncertain multivariable systems with time-delay , 2007 .

[9]  M. Mahmoud,et al.  H∞-Controllers for Time-Delay Systems Using Linear Matrix Inequalities , 1999 .

[10]  Michael V. Basin,et al.  On delay-dependent stability for vector nonlinear stochastic delay-difference equations with Volterra diffusion term , 2007, Syst. Control. Lett..

[11]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[12]  J. Shamma.  Optimization of the l∞-induced norm under full state feedback , 1996, IEEE Trans. Autom. Control..

[13]  Tong Heng Lee,et al.  A less conservative robust stability test for linear uncertain time-delay systems , 2006, IEEE Trans. Autom. Control..

[14]  Mathukumalli Vidyasagar,et al.  Optimal rejection of persistent bounded disturbances , 1986 .

[15]  Panos J. Antsaklis,et al.  Set-valued observer design for a class of uncertain linear systems with persistent disturbance , 2003, Proceedings of the 2003 American Control Conference, 2003..

[16]  E. Fridman,et al.  Delay-dependent stability and H 1 control : constant and time-varying delays , 2002 .

[17]  Yuechao Wang,et al.  An LMI approach to stability of systems with severe time-delay , 2004, IEEE Transactions on Automatic Control.

[18]  Qiang Zhang,et al.  Generalized LMI-based approach to the global asymptotic stability of discrete-time delayed recurrent neural networks , 2008 .

[19]  Magdi S. Mahmoud,et al.  New results on delay-dependent control of time-delay systems , 2005, IEEE Transactions on Automatic Control.

[20]  M. Mahmoud.  Robust Control and Filtering for Time-Delay Systems , 2000 .

[21]  Yuanqing Xia,et al.  Delay-dependent robust ℋ ∞ control for uncertain stochastic time-delay system , 2008, Int. J. Syst. Sci..

[22]  I. Postlethwaite,et al.  Linear Matrix Inequalities in Control , 2007 .

[23]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[24]  Chien-Yu Lu.  A delay-dependent approach to robust control for neutral uncertain neural networks with mixed interval time-varying delays , 2011 .

[25]  Vladimir L. Kharitonov,et al.  Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems , 2003, Autom..

[26]  Yun Chen,et al.  Delay-Dependent Robust Control for Uncertain Stochastic Time-Delay Systems , 2008 .

[27]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[28]  J. Pearson,et al.  l^{1} -optimal feedback controllers for MIMO discrete-time systems , 1987 .

[29]  A. Rodkina,et al.  On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays , 2008 .

[30]  Munther A. Dahleh,et al.  State feedback e 1 -optimal controllers can be dynamic , 1992 .

[31]  Huijun Gao,et al.  Stabilization of Networked Control Systems With a New Delay Characterization , 2008, IEEE Transactions on Automatic Control.

[32]  Yuanqing Xia,et al.  Robust delay-dependent sliding mode control for uncertain time-delay systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[33]  Qing-Long Han,et al.  On Hinfinity control for linear systems with interval time-varying delay , 2005, Autom..

[34]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[35]  Tianguang Chu,et al.  Persistent bounded disturbance rejection for impulsive systems , 2003 .

[36]  Lihua Xie,et al.  Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay , 2007, IEEE Transactions on Automatic Control.

[37]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[38]  Michael V. Basin,et al.  On delay-dependent stability for a class of nonlinear stochastic delay-differential equations , 2006, Math. Control. Signals Syst..

[39]  Yuanqing Xia,et al.  New stability and stabilization conditions for systems with time-delay , 2007, Int. J. Syst. Sci..