Event-Triggered Control of Nonlinear Systems: A Small-Gain Approach

Abstract

This chapter studies the event-triggered control problem for nonlinear systems with input-to-state stability (ISS) as the basic notion and the ISS small-gain theorem as a tool. The contribution of this book chapter is twofold. First, an ISS gain condition is proposed for event-triggered control of nonlinear uncertain 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 measurement 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. Self-triggered control designs for systems under external disturbance are also developed in the ISS-based framework. Second, this chapter introduces a new design method for input-to-state stabilization of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the measurement error as the input can be designed to satisfy the proposed condition for event-triggered control.