Periodic asymptotic controllability of switched systems

This paper deals with the dynamical behavior of switched systems, formed by a finite number of linear vector fields. In particular, we review and present in a systematic way some definitions and some results, representing useful tools for the investigation of the stability properties. We also provide a thoughtful comparison among the notions of loss and gain of stability, and asymptotic controllability at the origin and at the infinity. Finally we examine a number of new example