  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 that the lifted system dynamics remains linear, we
establish a method based on reachability computations to characterize and
compute the maximal admissible invariant set, which coincides with the domain
of attraction when the system is asymptotically stable. After developing the
necessary theoretical background, we propose algorithmic procedures for its
exact computation, based on linear or semidefinite programs. The approach is
illustrated in several numerical examples.
