A stratified geometric approach to the disturbance decoupling problem with stability for switched systems over digraphs

This chapter considers the disturbance decoupling problem with stability (more precisely, eigenvalue assignment) 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 the main tool for the definition of appropriate geometric properties tailored to the considered setup. Appropriate forms of feedback laws that achieve disturbance decoupling with spectral assignability under certain classes of admissible switching signals are characterized in terms of two distinct notions of controlled invariance. The result specializes more general approaches based on robust controlled invariance by exploiting the graph structure of the switching topology.