Lyapunov stability of nonlinear systems with delayed impulses: An event‐triggered impulsive control approach

Abstract In this paper, we employ an event‐triggered impulsive control (ETIC) approach to examine the Lyapunov stability of nonlinear systems subject to delayed impulses. Leveraging impulse control theory, an event‐triggered mechanism (ETM) based on the Lyapunov function is developed, and sufficient conditions are established to ensure both uniform stability (US) and global asymptotic stability (GAS) of the considered system while excluding Zeno behavior. It has been shown that the stability conditions depend not only on the ETM but also on time delays. Subsequently, we apply these theoretical findings to a nonlinear impulsive control system and design the appropriate ETM and impulse controllers according to the linear matrix inequality (LMI) to realize the GAS. The controller accounts for the impact of delays and is activated solely upon event triggering. Finally, two numerical simulations are shown to confirm the effectiveness of the proposed approach.