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

Abstract

SUMMARYThis 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.