Finite-Time H∞ Control for Time-Delayed Stochastic Systems with Markovian Switching

Abstract

This paper studies the problem of finite-time $H_{\infty }$ control for time-delayed Itô stochastic systems with Markovian switching. By using the appropriate Lyapunov-Krasovskii functional and free-weighting matrix techniques, some sufficient conditions of finite-time stability for time-delayed stochastic systems with Markovian switching are proposed. Based on constructing new Lyapunov-Krasovskii functional, the mode-dependent state feedback controller for the finite-time $H_{\infty }$ control is obtained. Simulation results illustrate the effectiveness of the proposed method.