Period-Sampled Switching Event-Triggered Control of Switched Linear Systems

This brief focuses on the event-triggered control (ETC) problem for a class of switched linear systems in which the controller updates the sampled information of both the system states and the switching signal only at the moment of event triggering. When the system switching occurs in the holding interval, the controller does not update the switching signal, which leads to the asynchronous switching behavior between the controller and the switched system. To solve the problem, we develop a new switching event-triggered mechanism (ETM) with periodic sampling by introducing a relative threshold function and an asynchronous related jump function with a tuning parameter. This period-sampled switching ETM can save computing resources and avoid Zeno behavior. Then, based on the multiple Lyapunov functional technique and the average dwell time (ADT) method, some sufficient conditions for global uniform exponential stability (GUES) of the closed-loop system are proposed. Besides, the corresponding solvability conditions for the co-design of the switching signal and the event-triggered controller are established. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.