Title: Invariance in Constrained Switching,
Abstract: We study discrete time linear constrained switching systems with additive
disturbances, in which the switching may be on the system matrices, the
disturbance sets, the state constraint sets or a combination of the above. In
our general setting, a switching sequence is admissible if it is accepted by an
automaton. For this family of systems, stability does not necessarily imply the
existence of an invariant set. Nevertheless, it does imply the existence of an
invariant multi-set, which is a relaxation of invariance and the object of our
work. First, we establish basic results concerning the characterization,
approximation and computation of the minimal and the maximal admissible
invariant multi-set. Second, by exploiting the topological properties of the
directed graph which defines the switching constraints, we propose invariant
multi-set constructions with several benefits. We illustrate our results in
benchmark problems in control.