Robust delay‐dependent ℋ︁∞ control of time‐delay systems with state and input delays

Abstract

AbstractThis paper studies the design problem of robust delay‐dependent ℋ︁∞ controller for a class of time‐delay control systems with time‐varying state and input delays, which are assumed to be noncoincident. The system is subject to norm‐bounded uncertainties and ℒ︁2 disturbances. Based on the selection of an augmented form of Lyapunov–Krasovskii (L‐K) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time‐delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay‐dependent criteria are developed for a stabilizing ℋ︁∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm‐bounded uncertainties, both the BRL and ℋ︁∞ stabilization criteria are easily extended by employing a well‐known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature. Copyright © 2010 John Wiley & Sons, Ltd.