Formula omitted]-dominant switched linear systems

Abstract

This paper studies the asymptotic behavior of switched linear systems, beyond classical stability. We focus on systems having a low-dimensional asymptotic behavior, that is, systems whose trajectories converge to a common time-varying low-dimensional subspace. We introduce the concept of path-complete p-dominance for switched linear systems, which generalizes the approach of quadratic Lyapunov theory by replacing the contracting ellipsoids by families of quadratic cones whose contraction properties are dictated by an automaton. We show that path-complete p-dominant switched linear systems are exactly the ones that have a p-dimensional asymptotic behavior. Then, we describe an algorithm for the computation of the cones involved in the property of p-dominance. This allows us to provide an algorithmic framework for the analysis of switched linear systems with a low-dimensional asymptotic behavior.