Event-Triggered Impulsive Control for Nonlinear Systems with Actuation Delays

TL;DR

This paper introduces two event-triggered impulsive control algorithms for nonlinear systems with actuation delays, ensuring stability and avoiding Zeno behavior, validated through theoretical analysis and an example.

Contribution

It proposes novel event-triggering algorithms for impulsive control with delays, providing stability conditions and bounds to prevent Zeno phenomena.

Findings

Algorithms ensure asymptotic stability.

Lower bounds prevent Zeno behavior.

Example confirms effectiveness.

Abstract

This paper studies impulsive stabilization of nonlinear systems. We propose two types of event-triggering algorithms to update the impulsive control signals with actuation delays. The first algorithm is based on continuous event detection, while the second type makes decision about updating the impulsive control inputs according to periodic event detection. Sufficient conditions are derived to ensure asymptotic stability of the impulsive control systems with the designed event-triggering algorithms. Lower bounds of the time period between two consecutive events are also obtained, so that the closed-loop impulsive systems are free of Zeno behavior. That is to say that the pulse phenomena are excluded from the event-triggered impulsive control systems, in the community of impulsive differential equations. An illustrative example demonstrates effectiveness of the proposed algorithms and our theoretical results.