H∞ control for networked switched systems with mixed switching law and an event-triggered communication mechanism

This paper studies the event-triggered control problem for networked switched systems with a mixed time and state-dependent switching law. By the event-triggering strategies, only necessary samplings of feedback signals are determined to be released. The advantages are that redundant transmissions and updates can be reduced. By the adopted switching law, each sub-system will work for a minimum dwell time, and then a state-dependent switching starts to work. Specifically, by using discrete event-triggering strategies and considering the effects of transmission delays, a time-delay closed-loop switched system is first established. Then, by utilising multiple Lyapunov functions method, sufficient conditions are presented to ensure the stability of the closed-loop switched system with a certain performance level. In particular, since the switching instants and the event-triggered instants may be coupled, typical cases are discussed in detail. Moreover, the co-design conditions for state-feedback sub-controller gains and event-triggering parameters are developed. Finally, the effectiveness of the proposed method is verified by numerical simulations.