A New Method to Reliable H∞ Control of Nonlinear Stochastic Systems with Actuator Faults

Abstract

By presenting actuator faults as a Markov process, this paper is concerned with the reliable $$H_{\infty }$$ control of stochastic nonlinear systems which are approximated by an Ito-type Takagi–Sugeno fuzzy structure with an affine structure. The objective is to probe a static output $$H_\infty$$ control scheme such that the resultant closed-loop system is stochastically stable with the required $$H_\infty$$ performance. To realize this aim, with the help of Lyapunov stability and robust methodologies, a new method to solve the static output controller is established in the framework of linear matrix inequalities. Compared with the existing result, the proposed method renders a less conservative $$H_\infty$$ performance level $$\gamma$$ , which is verified by numerical examples.