Switching event‐triggering mechanisms for integral input‐to‐state stable nonlinear systems

Abstract

This article studies the event-triggered control problem for nonlinear systems that are merely integral input-to-state stable (iISS) with respect to measurement errors and external inputs. By using the iISS Lyapunov function, which comes from a necessary and sufficient condition on iISS, an integral-based event-triggering mechanism is introduced to compensate the effects of measurement errors. Under some assumptions on the gains of the iISS Lyapunov function, both the closed-loop iISS and Zeno-freeness are proved when the external inputs are measurable. In the presence of unknown disturbances, a novel switching event-triggering mechanism is designed based on the relationship between the transmitted state and some threshold constant. Subsequently, the corresponding lower bound of inter-event times is given explicitly to ensure Zeno-freeness. It is shown that the proposed switching mechanism can be applicable to the nonlinear systems where some existing event-triggering mechanisms are invalid in avoiding Zeno behavior. Finally, numerical simulations are provided to illustrate the efficiency and feasibility of the obtained results.