Asynchronous Control for 2 $$ 2 $$ -D Switched Systems With Quasi-Time-Dependent Lyapunov Function and Weighted Average Dwell Time Strategy

This paper focuses on the asynchronous control for a specific category of two-dimensional ($2$-D) switched systems with the weighted average dwell time strategy. The system is described using the renowned Fornasini-Marchesini local state-space model. The control signal for the switching mechanism incorporates time delays, which result in asynchronism between the controllers and subsystems. By using the weighted average dwell time strategy and a switched quasi-time-dependent Lyapunov functional method, sufficient conditions for stabilizing the $2$-D switched system with asynchronous switching are formulated. Based on the stabilization result, the state-feedback controllers are designed to ensure $H_{\infty }$ performance and asymptotic stability of the corresponding closed-loop system. An illustrative example is presented to validate the efficacy of the proposed control scheme.