Event-triggered control of switched linear systems with state-dependent switching law and unstabilizable modes

This paper studies the event-triggered control of switched linear system with state-dependent switching law. A dynamic term is introduced to the switching law to acclimatize the dynamic mode-dependent event-triggered controller. Besides, neither the switching law nor the controller needs continuous detection of the system states. Because of the event-triggered and sampling behavior of the controller, asynchronous between the controller and the system modes are encountered. A new multiple Lyapunov functional is proposed to appropriately characterize the synchronous and asynchronous working modes of the system, and a sufficient exponential stability condition is obtained, which is applicable for the cases when some modes or all modes of the switched system are unstabilizable. Moreover, the event-triggered control and switching law parameters are jointly designed using linear matrix inequalities. Numerical and comparison studies are offered to provide the validity and superiority of the result.