H∞ tracking control for time-delay systems with Markovian jumping parameters

This paper is concerned with the H∞ tracking control problem for linear time-delay systems with Markovian jumping parameters. The objective is to design state-feedback mode-dependent controllers such that the resulting closed-loop system is stochastically stable and its state follows a reference signal. Based on the Lyapunov-Krasovskii functional method together with the delay-partitioning technique, delay-dependent conditions for the existence of the desired controllers are obtained in terms of linear matrix inequalities. In addition, a new stability criterion for Markovian jump systems with constant delays is also given, which is less conservative than the recent ones in the literature. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.