Finite-time stability via event-triggered delayed impulse control for time-varying nonlinear impulsive systems

This article addresses the issue of finite-time stability (FTS) for time-varying nonlinear impulsive systems using event-triggered delayed impulse control (ETDIC). Unlike traditional time-triggered impulse control, event-triggered impulse control activates only when specific conditions are met, thereby reducing unnecessary computational and information service demands associated with time-triggered mechanisms. To achieve this, we propose a Lyapunov function-based event-triggered mechanism that effectively handles the impact of time-delay in impulses and avoids Zeno behavior. Moreover, the results indicate that the time-delay in impulses can help stabilize the system and enhance its properties. We then apply the theoretical findings to complex neural networks and design ETDIC strategies to achieve FTS for these systems. Finally, the feasibility of the proposed scheme is demonstrated through two simulation examples.