Robust Nonfragile Guaranteed Cost Control for Uncertain Fuzzy Markov Jump Systems with Time-Varying Delays

Abstract

This paper aims to investigate the problem of robust nonfragile guaranteed cost control for uncertain discrete-time Takagi–Sugeno fuzzy systems with Markov jumping parameters and time-varying delay. A nonfragile fuzzy-basis-dependent and mode-dependent controller is designed and a sufficient condition is developed to ensure that the resulting closed-loop system is robust asymptotically stable in mean square with guaranteed cost index not exceeding the specified upper bound. Subsequently, the controller gain and minimum upper bound of the guaranteed cost index can be obtained by solving a set of linear matrix inequalities. Compared with the existing literature, this paper enormously reduces the conservatism of the result obtained. Finally, numerical and practical examples are provided to demonstrate the performance of the proposed approach.