Optimal Guaranteed Cost Control of Uncertain Discrete Systems with Both State and Input Delays: New LMI-Based Characterization and Methods

This paper addresses the guaranteed cost control for a class of uncertain discrete-time systems with both state and input delays. New linear matrix inequalities (LMI) characterizations are proposed for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties. A procedure is given to select a suitable state feedback controller that minimizes a bound on a quadratic performance index. The result exhibits some favorable features in computation which is shown by a numerical example

[1]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[2]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[3]  H. Kokame,et al.  Stabilization of perturbed systems via linear optimal regulator , 1988 .

[4]  B. Barmish.  Necessary and sufficient conditions for quadratic stabilizability of an uncertain system , 1985 .

[5]  Ian R. Petersen,et al.  An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems , 2000 .

[6]  S.O.R. Moheimani,et al.  Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[7]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[8]  Ian R. Petersen,et al.  Optimal Guaranteed Cost Control of Discrete-time Uncertain Linear Systems 1 , 1993 .

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

[10]  Xiaoming Xu,et al.  The quadratic stability of a discrete-time system with structured uncertainties , 1999 .

[11]  Lihua Xie,et al.  Guaranteed cost control of uncertain discrete systems with delays , 2000 .

[12]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[13]  Li Yu,et al.  Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Systems Using Linear Matrix Inequalities , 2002 .

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

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

[16]  Ian R. Petersen,et al.  Optimal guaranteed cost control of discrete‐time uncertain linear systems , 1998 .

[17]  Li Yu,et al.  Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays , 2001, J. Frankl. Inst..

[18]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..