A Lyapunov‐Like Function‐Based Event‐Triggered Stabilization Scheme for Nonlinear Discrete‐Time Systems

Abstract

ABSTRACT This study investigates stabilization methodologies utilizing event‐triggered mechanisms tailored for specific discrete‐time nonlinear systems. A Lyapunov‐like stability theorem is first established, which relaxes the conventional strict monotonic decrease constraint on the energy function and extends the applicability of stability theory. Based on this Lyapunov‐like function, a novel event‐triggered mechanism is developed, from which a critical triggering threshold is derived. It is shown that asymptotic stability is ensured if the number of triggering events is bounded by , and finite‐time stability is achieved otherwise. The proposed triggering condition allows bounded increments of the Lyapunov‐like function between consecutive triggering instants and even permits it to temporarily exceed its value at the previous trigger. In addition, the obtained results avoid restrictive assumptions such as norm‐bounded nonlinearities and matching conditions, thus improving generality and applicability. To validate the efficiency of the proposed approach, two simulation examples are conducted at last.