Structural Properties of a Class of Linear Hybrid Systems and Output Feedback Stabilization

In this paper, we deal with the problem of output feedback stabilization for a class of linear hybrid systems. This problem is addressed by characterizing the structural properties of such a class of systems. Namely, reachability, controllability, stabilizability, observability, constructibility, and detectability are framed in terms of algebraic and geometric conditions on the data of the system. Two canonical forms, recalling the classical Kalman decompositions with respect to reachability and observability, are given. By taking advantage of this characterization, duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time-invariant output feedback compensator are stated. Compared with previous results, no assumption is needed on the plant about minimum phaseness, relative degree, or squareness.