On universal classes of Lyapunov functions for linear switched systems - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Automatica Year : 2023

On universal classes of Lyapunov functions for linear switched systems

Paolo Mason
Yacine Chitour

Abstract

In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous function for the $C^0$ topology of the unit sphere. On the other hand, we prove several obstructions for a class to be universal, showing, in particular, that families of piecewise-polynomial continuous functions whose construction involves at most $l$ polynomials of degree at most $m$ (for given positive integers $l,m$) cannot be universal.
Fichier principal
Vignette du fichier
Universal-preprint.pdf (287.62 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03753540 , version 1 (18-08-2022)

Licence

Attribution

Identifiers

Cite

Paolo Mason, Yacine Chitour, Mario Sigalotti. On universal classes of Lyapunov functions for linear switched systems. Automatica, 2023, 155, pp.111155. ⟨10.1016/j.automatica.2023.111155⟩. ⟨hal-03753540⟩
89 View
98 Download

Altmetric

Share

Gmail Facebook X LinkedIn More