Weighted $$\mathbf{H}_\infty$$ Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method

Abstract

In this paper, the issues about weighted $$H_\infty$$ performance analysis and $$H_\infty$$ control for the stochastic switched nonlinear systems (SSNSs) with multiplicative noise are investigated. The mode-dependent average dwell time (MDADT) method is used to deal with the switching in different modes. Firstly, we get a sufficient condition to show that the considered system with all stable subsystems achieves the exponential stability in mean square sense and a specified weighted $$H_\infty$$ performance, which is extended to the case that both stable and unstable subsystems coexist in terms of second-order Hamilton-Jacobi inequalities (HJIs). Then, by using Takagi-Sugeno (T-S) fuzzy approach, the $$H_\infty$$ controller for SSNSs is designed via solving a set of linear matrix inequalities (LMIs). Finally, an example is supplied to illustrate the effectiveness of our results.