Event-triggered stabilization of nonlinear systems by using fast-varying square wave dithers

Abstract

This paper studies static output-feedback stabilization of the second- and third-order (with relative degree 3) nonlinear systems by a fast-varying square wave dither with a high gain. Recently, a constructive time-delay approach to design such a fast-varying output-feedback controller for linear systems was suggested by using continuous measurements. In the present paper, we extend these results to the case where the measurements are sent to the controller via a communication network. The sampling intervals are expected to be small due to the rapidly oscillating high gains. To reduce the network load, we suggest a dynamic event-trigger (ET) via switching approach. We present the closed-loop system as a switching between the system under periodic sampling and the one under continuous event-trigger and take the maximum sampling preserving the stability as the lower bound of inter-event time. We construct appropriate coordinate transformations that cancel the high gains in the closed-loop system and apply the time-delay approach to periodic averaging of the system in new coordinates. By employing appropriate Lyapunov functionals, we derive linear matrix inequalities (LMIs) for finding efficient bounds on the dither frequencies and inter-event times that guarantee the stability of the original systems. Numerical examples illustrate the efficiency of the method.