A Converse Lyapunov Theorem for p-dominant Switched Linear Systems

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.