${\mathcal{L}}_{\infty}$ Control of Switched T-S Fuzzy Systems Under Relieved Asynchronous Switching: A Zonotope...

This article addresses the zonotopic ${\mathcal {L}}_{\infty } $ dynamic output-feedback control problem for discrete-time switched Takagi-Sugeno (T-S) fuzzy systems. To overcome the conservatism of existing methods, a novel relieved asynchronous average dwell time (ADT) switching scheme is proposed, which successfully eliminates the conventional restrictive requirement that the subsystem dwell time (DT) must strictly exceed the maximum asynchronous duration. First, state and output zonotopes are constructed, facilitating the introduction of multiple radius and center-distance functions. Distinct from Lyapunov-dependent approaches, by leveraging the radius- and center-distance-based analysis technique, sufficient conditions are derived to guarantee the dual convergence and the prescribed ${\mathcal {L}}_{\infty } $ performance of the zonotopes. Subsequently, building upon these zonotopic results, the allowable ADT switching signals and switched fuzzy dynamic output-feedback controllers are codesigned to achieve the stability of the closed-loop systems. Finally, the superiority and effectiveness of the proposed zonotopic control scheme are validated through an illustrative switched T-S fuzzy example.