Invariance principles for hybrid systems with connections to detectability and asymptotic stability

This paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The general invariance results are then specified to hybrid systems given by set-valued data. Further results involving invariance as well as observability, detectability, and asymptotic stability are given.