A small-gain approach to event-triggered control of nonlinear systems

This paper presents a new approach to event-triggered control of nonlinear systems. The study is directly based on the notion of input-to-state stability (ISS) and its essential relationship with robust stability. Our main result is an ISS gain condition for event-triggered control of nonlinear systems. It is proved that infinitely fast sampling can be avoided with an appropriately designed event triggering mechanism if the system is input-to-state stabilizable with the sampling error as the external input and the resulted ISS gain is Lipschitz on compact sets. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by ISS small-gain arguments.