Lyapunov Design for Event-Triggered Exponential Stabilization

TL;DR

This paper develops an event-triggered control strategy that ensures exponential stabilization of nonlinear systems, closely matching the convergence rate of the continuous-time control, thus bridging the gap between theoretical control design and digital implementation.

Contribution

It introduces a method to derive exponentially stabilizing event-triggered controllers from continuous-time Lyapunov-based controllers, maintaining similar convergence rates.

Findings

Event-triggered control can achieve exponential stabilization with arbitrary convergence rates.

The proposed method ensures digital implementation of continuous-time controllers without sacrificing stability.

The approach bridges the gap between theoretical control design and practical digital control systems.

Abstract

Control Lyapunov Functions (CLF) method gives a constructive tool for stabilization of nonlinear systems. To find a CLF, many methods have been proposed in the literature, e.g. backstepping for cascaded systems and sum of squares (SOS) programming for polynomial systems. Dealing with continuous-time systems, the CLF-based controller is also continuous-time, whereas practical implementation on a digital platform requires sampled-time control. In this paper, we show that if the continuous-time controller provides exponential stabilization, then an exponentially stabilizing event-triggered control strategy exists with the convergence rate arbitrarily close to the rate of the continuous-time system.