Delay-Dependent Stability and Robust H ∞ Control for Discrete-Time Markovian Jump Linear Systems with Mode-Dependent Delays

Abstract

In this paper, the stability, stabilization and Hinfin control problems for a class of uncertain discrete-time Markovian jump linear systems with mode-dependent time-delays are investigated. The key features of the approach include the introduction of a new stochastic Lyapunov functional and some free weighting matrices involved in a special inequality. New Delay-dependent sufficient conditions for the problems are developed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.