# Lyapunov Event-triggered Stabilization with a Known Convergence Rate

## TL;DR

This paper demonstrates that event-triggered controllers can achieve the same exponential convergence rate as continuous-time controllers using Control Lyapunov Functions, ensuring positive dwell times and stability.

## Contribution

It proves the existence of event-triggered and self-triggered controllers that guarantee a predefined convergence rate with positive dwell times, extending CLF-based stabilization.

## Key findings

- Event-triggered controllers can match the convergence rate of continuous controllers.
- Positive dwell times are guaranteed between events.
- Existence of self-triggered and periodic controllers with known convergence rates.

## Abstract

A constructive tool of nonlinear control systems design, the method of Control Lyapunov Functions (CLF) has found numerous applications in stabilization problems for continuous time, discrete-time and hybrid systems. In this paper, we address the fundamental question: given a CLF, corresponding to the continuous-time controller with some predefined (e.g. exponential) convergence rate, can the same convergence rate be provided by an event-triggered controller? Under certain assumptions, we give an affirmative answer to this question and show that the corresponding event-based controllers provide positive dwelltimes between the consecutive events. Furthermore, we prove the existence of self-triggered and periodic event-triggered controllers, providing stabilization with a known convergence rate.