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We characterize and compute the maximal admissible positively invariant setfor asymptotically stable constrained switching linear systems. Motivated bypractical problems found, e.g., in obstacle avoidance, power electronics andnonlinear switching systems, in our setting the constraint set is formed by afinite number of polynomial inequalities. First, we observe that the so-calledVeronese lifting allows to represent the constraint set as a polyhedral set.Next, by exploiting the fact that the lifted system dynamics remains linear, weestablish a method based on reachability computations to characterize andcompute the maximal admissible invariant set, which coincides with the domainof attraction when the system is asymptotically stable. After developing thenecessary theoretical background, we propose algorithmic procedures for itsexact computation, based on linear or semidefinite programs. The approach isillustrated in several numerical examples.

Computing the domain of attraction of switching systems subject to non-convex constraints