Comparison of path-complete Lyapunov functions via template-dependent lifts. (November 2022)

• Record Type: Journal Article
• Authors: Debauche, Virginie; Della Rossa, Matteo; Jungers, Raphaël M.
• Is Part Of: Nonlinear analysis. Volume 46(2022)
• Publication Date: 2022-11
• Subjects: Path-complete methods -- Switched systems -- Positive systems -- Lifts; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2022.101237
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper investigates, in the context of discrete-time switched systems, the problem of comparison for path-complete stability certificates. We introduce and study abstract operations on path-complete graphs, called lifts, which allow us to recover previous results in a general framework. Moreover, this approach highlights the existing relations between the analytical properties of the chosen set of candidate Lyapunov functions (the template ) and the admissibility of certain lifts. This provides a new methodology for the characterization of the ordering relation of path-complete Lyapunov functions criteria, when a particular template is chosen. We apply our results to specific templates, notably the sets of primal and dual copositive norms, providing new stability certificates for positive switched systems. These tools are finally illustrated with the aim of numerical examples.