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

ABSTRACT This paper focuses on the asynchronous control for a specific category of two‐dimensional (‐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 ‐D switched system with asynchronous switching are formulated. Based on the stabilization result, the state‐feedback controllers are designed to ensure performance and asymptotic stability of the corresponding closed‐loop system. An illustrative example is presented to validate the efficacy of the proposed control scheme.