The disturbance decoupling problem for switched discrete-time linear systems over digraphs: A stratified geometric approach

This paper considers the disturbance decoupling problem for switched discrete-time linear systems, where switching occurs within a set of admissible transitions defined via a weighted directed graph. The concept of subspace arrangement, as a collection of linear subspaces, is employed as a main tool for the definition of geometric properties tailored to switched systems over digraphs. Appropriate forms of feedback laws that achieve disturbance decoupling under certain classes of admissible switching signals are characterized in terms of strong and weak notions of controlled invariance. The result extends previous approaches based on robust controlled invariance, to the special class of switched discrete-time linear systems over digraphs based on stratified controlled invariance.