On feedback stabilization of linear switched systems via switching signal control

TL;DR

This paper investigates how to stabilize linear switched systems by designing feedback-based switching signals, introducing new algorithms and analyzing their mathematical properties to advance control theory understanding.

Contribution

It presents novel algorithms for feedback stabilization, analyzes complex mathematical features, and explores equivalences between stabilizability concepts in switched systems.

Findings

Proved complexity results for stabilization

Established (in-)equivalence between stabilizability notions

Provided a case study on a paradigmatic example

Abstract

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.