A hybrid event-triggered stabilization approach for switched systems under asynchronous switching and its application

This paper investigates the stabilization problem of switched systems with mismatched modes by an event-triggered control approach. A hybrid event-triggered scheme (HETS) with a dynamically adjustable threshold is newly proposed, which combines periodic sampling, continuous event-trigger and slow switching. It is assumed that the modes and states of the controller are updated only at each triggering instant, so the situation of asynchronous switching could arise. Compared with the control strategy under static HETS, the proposed hybrid event-triggered control strategy has the advantage of potentially speeding up the stabilization while reducing the communication burden. To ease the analysis, the closed-loop system is accordingly represented as a combination of the switched system with a periodically sampled control input and the one with a continuously event-triggered control input. By considering input delay information in the construction of multiple Lyapunov-Krasovskii functional (LKF), a discontinuous and non-positive definite LKF is developed to establish sufficient conditions on the exponential stability for the closed-loop switched system. The design method of the desired controller and HETS is then provided. Finally, the result obtained in this paper is applied to a networked continuous stirred tank reactors system.