\(H_\infty\) control for T-S fuzzy singularly perturbed switched systems (Q1992527)

Summary: This paper is concerned with the design of fuzzy controller with guaranteed \(H_{\infty}\) performance for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. First, by using the average dwell time approach together with the piecewise Lyapunov function technique, a state feedback controller that depends on the singular perturbation parameter \(\varepsilon\) is developed. This controller is shown to work well for all \(\varepsilon \in(0, \varepsilon_0]\). Then, for sufficiently small \(\varepsilon \), an \(\varepsilon \)-independent controller design method is proposed. Furthermore, under the \(\varepsilon \)-independent controller, the \(\varepsilon \)-bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to evaluate the feasibility and effectiveness of the obtained results.