Uniformity of Controllability and Stabilization of Switched Linear Time-Varying Systems

We consider the stabilization of systems that switch among an arbitrary number of linear time-varying subsystems, which cannot be stabilized by simply stabilizing all the subsystems even if their dwell time is large enough. We introduce a uniform controllability condition for all the subsystems under which we can design controllers for the subsystems such that the closed-loop subsystems are exponentially stable, and their state transition matrices have uniformly bounded magnitudes. We prove using this uniformity condition that the systems considered are exponentially stabilizable if the switching signals have a known or unknown positive average dwell time.