Event-triggered control for nonlinear systems involving hybrid impulses

Abstract

In this paper, we apply event-triggered control to nonlinear systems with impulses, and investigate the problem of ensuring globally exponential stability (GES) of the systems, where events and impulses may occur at different time. Moreover, two types of impulses (i.e., stabilizing and destabilizing) can coexist. On the basis of Lyapunov method and impulsive control theory, some sufficient conditions ensuring GES are derived, and the Zeno behaviour can be excluded. These conditions are presented in the form of linear matrix inequalities (LMI). In particular, inspired by average dwell-time methods, conditions for restriction of impulses are proposed, which guarantee GES of nonlinear systems involving single stabilizing and destabilizing or multiple impulses, respectively. Furthermore, the problem of designing event-triggered mechanism and control gains are solved by using LMI method. Lastly, two numerical simulation examples are given to represent the effectiveness of our results.