We study discrete time linear switching systems subject to additive disturbances. We consider two types of constraints, namely on the states and on the switching signal. A switching sequence is admissible if it is accepted by an automaton. Contrary to the arbitrary switching case, stability does not imply the existence of an invariant 1  set. In this article, we propose a generalization of a bounded invariant set, namely, the notion of an invariant multi-set and show its significance in terms of dynamical systems. Under standard assumptions, we provide an iterative algorithm to approximate the minimal invariant multi-set with a guarantee of accuracy and an algorithm to compute the maximal invariant multi-set. Application of the established framework to switching systems with minimum dwell time reveals potential computational benefits and allows formulations of more refined notions.
['Nikolaos Athanasopoulos', 'Konstantinos Smpoukis', 'Raphaël M. Jungers']
Safety and invariance for constrained switching systems