On the Search for Equilibrium Points of Switched Affine Systems

TL;DR

This paper develops algorithms to identify and verify equilibrium points in switched affine systems, facilitating the design of stabilizing controllers when the goal equilibrium is partially specified or constrained.

Contribution

It introduces methods to determine if a goal is an equilibrium and to jointly find equilibrium points and stabilizing switching functions.

Findings

Algorithms successfully identify equilibrium points in complex systems.

Joint search for equilibrium points and switching functions improves control design.

Enhanced ability to handle partially specified goals or constraints.

Abstract

One of the main aspects of switched affine systems that makes their stabilizability study intricate is the existence of (generally) infinitely many equilibrium points in the state space. Thus, prior to designing the switched control, the user must specify one of these equilibrium points to be the goal or reference. This can be a cumbersome task, especially if this goal is partially given or only defined as a set of constraints. To tackle this issue, in this paper we describe algorithms that can determine whether a given goal is an equilibrium point of the system and also jointly search for equilibrium points and design globally stabilizing switching functions.