# Self-triggered stabilizing controllers for linear continuous-time systems

## TL;DR

This paper introduces a self-triggered control method for linear continuous-time systems that predicts control update events using a pseudo-Lyapunov function, reducing communication while ensuring stability.

## Contribution

It develops a self-triggered control algorithm based on a pseudo-Lyapunov function and a hybrid root-finding method, improving efficiency over traditional event-triggered control.

## Key findings

- Reduces communication between controller and plant
- Maintains system stability with fewer updates
- Uses a hybrid root-finding algorithm for event prediction

## Abstract

Self-triggered control is an improvement on event-triggered control methods. Unlike the latter, self-triggered control does not require monitoring the behavior of the system constantly. Instead, self-triggered algorithms predict the events at which the control law has to be updated before they happen, relying on system model and past information.\\ In this work, we present a self-triggered version of an event-triggered control method in which events are generated when a pseudo-Lyapunov function (PLF) associated with the system increases up to a certain limit. This approach has been shown to considerably decrease the communications between the controller and the plant, while maintaining system stability. To predict the intersections between the PLF and the upper limit, we use a simple and fast root-finding algorithm. The algorithm mixes the global convergence properties of the bisection and the fast convergence properties of the Newton-Raphson method. \\ Moreover, to ensure the convergence of the method, the initial iterate of the algorithm is found through a minimization algorithm.