Non-fragile robust stabilization and H∞ control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances

Abstract

This paper considers the problems of non-fragile robust stabilization and H∞ control for uncertain stochastic time delay systems with Markovian jump parameters and nonlinear disturbances. The parameter uncertainties are assumed to be time-varying norm bounded appearing in both state and input matrices. The purpose of the non-fragile robust stabilization problem is to design a memoryless non-fragile state feedback controller such that the closed-loop system is robustly stochastically stable for all admissible uncertainties in both the system and controller. In addition to the aforementioned requirement, a prescribed H∞ performance level is required to be achieved for the non-fragile robust H∞ control problem. With the use of the Lyapunov-Krasovskii functional method and free-weighting matrices, delay-dependent sufficient conditions for the solvability of these problems are obtained in terms of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.