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We characterize and compute the maximal admissible positively invariant set for asymptotically stable constrained switching linear systems. Motivated by practical problems found, e.g., in obstacle avoidance, power electronics and nonlinear switching systems, in our setting the constraint set is formed by a finite number of polynomial inequalities. First, we observe that the so-called Veronese lifting allows to represent the constraint set as a polyhedral set. Next, by exploiting the fact thatdoi:10.1145/2883817.2883823 dblp:conf/hybrid/AthanasopoulosJ16 fatcat:2vrv3ebhefcsdplzhxbgpq4bkm