Robust Delay-Dependent $H_{\infty }$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters

The problem of robust mode-dependent delayed state feedback H_∞ control is investigated for a class of uncertain time-delay systems with Markovian switching parameters and mixed discrete, neutral, and distributed delays. Based on the Lyapunov-Krasovskii functional theory, new required sufficient conditions are established in terms of delay-dependent linear matrix inequalities for the stochastic stability and stabilization of the considered system using some free matrices. The desired control is derived based on a convex optimization method such that the resulting closed-loop system is stochastically stable and satisfies a prescribed level of H_∞ performance, simultaneously. Finally, two numerical examples are given to illustrate the effectiveness of our approach.