Abstract
In this paper, asymptotic stability, $$l_2$$ -gain analysis and $$H_{\infty }$$ controller design problems of discrete-time switched T–S fuzzy systems are considered. A dwell-time-fuzzy-basis-dependent multiple Lyapunov functions (DTFBDLFs) approach is first proposed. Via the DTFBDLFs approach and T–S fuzzy model, convex sufficient conditions on stability and $$l_2$$ -gain performance of discrete-time switched nonlinear systems with dwell time are derived. A dwell-time-dependent fuzzy controller is also first proposed. Via the designed controller and T–S fuzzy model, stability and $$l_2$$ -gain performance of the closed-loop system under asynchronous switching can be guaranteed. The constructed DTFBDLF keeps decreasing along with the time. The obtained $$H_{\infty }$$ performance index is standard. All the results are presented in terms of linear matrix inequalities (LMIs). Two numerical examples are provided to show the advantage of DTFBDLFs approach and the effectiveness of the results.
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