Output regulation for a class of linear hybrid systems. Part 2: stabilization

This paper reports some stabilization results for a class of hybrid linear systems whose jumps are determined by time only. Linearity of the resulting closed-loop system implies that global asymptotic and incremental stability are achieved at the same time. In turn, incremental stability allows for the solution of a recently considered output regulation problem by coupling a suitable steady state generator (described in a companion paper) and the stabilizer from this paper. It is remarked that stabilization and regulation are achieved for general MIMO plants without relying on minimum phase, relative degree or squareness assumptions.