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

Abstract

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.