Invariance results for constrained switched systems

"In this paper we address invariance principles for nonlinear switched systems with otherwise arbitrary compact index set and with constrained switchings. We present an extension of LaSalle's invariance principle for these systems and derive by using detectability notions some convergence and asymptotic stability criteria. These results enable to take into account in the analysis of stability not only state-dependent constraints but also to treat the case in which the switching logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems."