Stability of Nonlinear Systems via Event‐Triggered Impulsive Control

ABSTRACT This paper investigates the stability problem of nonlinear systems based on the impulsive control (IC) theory and three‐level event‐triggered impulsive control mechanism (three‐ETM), and derives sufficient conditions for the asymptotic stability (AS), finite‐time stability (FTS), and finite‐time contraction stability (FTCS) of the system. Within the framework of three‐ETM, the proposed approach not only effectively avoids Zeno behavior but also establishes the intrinsic relationships among event‐triggered parameters, impulsive delay, and impulsive intensity. Furthermore, the theoretical results are applied to the stabilization of a class of impulsive systems with uncertainty parameters, and relevant stability conditions are established based on linear matrix inequalities (LMI). Finally, two numerical examples are provided to compare and analyze the proposed method with the traditional ETM. The results demonstrate that the three‐ETM is more effective in ensuring system performance.