A converse Lyapunov theorem for $p$-dominant switched linear systems

Berger, Guillaume;Jungers, Raphaël
(2019) 2019 18th European Control Conference (ECC) — Location: Naples, Italy (25.June.2019)

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Abstract
We study the path-complete $p$-contraction property for switched linear systems, which is a generalization of the notion of positive systems. We show on examples that this property is indeed useful for describing convergence properties, like $p$-dominance, that classical positivity cannot handle. We then provide a Converse Lyapunov Theorem, showing that, contrary to positivity, any $p$-dominant switched system must possess the path-complete $p$-contraction property with quadratic cones.
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Berger, G., & Jungers, R. (2019). A converse Lyapunov theorem for $p$-dominant switched linear systems. 2019 18th European Control Conference (ECC), 1263-1268. https://doi.org/10.23919/ECC.2019.8795923 (Original work published 2019)