Affine characterizations of minimum and mode-dependent dwell-times for uncertain linear switched systems

TL;DR

This paper introduces a novel Lyapunov looped-functional approach to characterize minimum and mode-dependent dwell-times in uncertain linear switched systems, resulting in affine stability conditions that improve analysis and design.

Contribution

It develops a new affine stability condition framework using Lyapunov looped-functionals, enabling better handling of uncertainties in dwell-time analysis.

Findings

Conditions are expressed as infinite-dimensional LMIs solvable via sum-of-squares techniques.

The approach effectively handles uncertainties in switched systems.

Numerical examples demonstrate the method's efficiency and accuracy.

Abstract

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. The proposed technique is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach.