Dissipative control of switched nonlinear systems with sliding mode: an event-triggered control scheme

This paper introduces the event-triggered scheme to study the problems of dissipative control and dissipativity-based sliding mode control (SMC) for switched nonlinear systems. Firstly, based on a designed event-triggered scheme, a piecewise continuous state feedback controller is constructed; sufficient conditions for $$\left( Q,S,R\right) $$ - $$\alpha $$ -dissipativity of the resulting system are derived by the approaches of a switched Lyapunov function and an average dwell time. Secondly, these two methods are extended to the study of $$H_\infty $$ performance and passive performance; the corresponding sufficient conditions are provided. Thirdly, the dissipative control problem is solved by introducing an event-triggered scheme into SMC method. Sufficient conditions for dissipativity of the resulting system are derived, and an SMC law is designed to guarantee the reachability. At the end of this paper, the correctness of the proposed methods is proved by two numerical examples.