Stabilizability and practical stabilizability of continuous-time switched systems: A unified view

There has been increasing interest in the stability analysis and design problems of switched systems during the past two decades. In such problems, it is usually assumed that all subsystems have a common equilibrium. Recently, switched systems without common equilibria have been observed to exhibit similar convergent behavior under appropriate switching laws. Such behavior is called practical stability. In this paper, we report some recent developments on practical stabilization of continuous-time switched systems. Besides formally introducing some practical stabilizability concepts, we delineate the connections and differences between practical and conventional stabilizability. In particular, we show that the study of practical stabilizability not only extends the stability research to more general classes of switched systems, but also makes switching control easier and more practical to implement. Four switching control problems are presented to demonstrate the importance and relevance of practical stabilization.