Output stabilization of switching systems with linear discrete-time modes

The discrete component of the hybrid state of a discrete-time linear switching system is assumed uncontrolled and unobserved. Conditions of stabilizability for this class of systems are given in terms of a new definition of control invariance, based on the realization of a discrete observer that permits reconstruction of the discrete state in certain intervals of the time basis. The paper highlights the relationship between the minimum dwell time of the system and its stabilizability. An almost complete characterization of stabilizability is offered in terms of certain subsets of the continuous state space. These sets are amenable to tractable parametric procedures for controller synthesis.