Normal forms of matrix words for stability analysis of discrete-time switched linear systems
Résumé
In this paper, we propose a new method for investigating the stability
of discrete-time switched linear systems by means of linear algebra
techniques. Exponential stability of such systems is equivalent to the
existence of solutions of linear matrix inequalities indexed by matrix
words, i.e., products of matrices of the sub-systems). Our method
consists in using the link between this characterization of
exponential stability and linear dependency among matrix words. In
particular, we introduce a criterion to reduce drastically the number
of linear matrix inequalities, by removing redundant ones. This is
achieved by eliminating matrix words that depend on the others. From
this criterion, we also relate exponential stability to quadratic
stability of another switched system. An example is given to
illustrate our methods.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)
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