Delay‐dependent robust<i>H</i>_∞control for uncertain singular time‐delay system with Markovian jumping parameters

Abstract

SUMMARY The problem of robust H ∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H ∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley &amp; Sons, Ltd.