Results on convergence in hybrid systems via detectability and an invariance principle

Two invariance principles for generalized hybrid systems are presented. One version involves the use of a nonincreasing function, like in the original work of LaSalle. The other version involves "meagreness" conditions. These principles characterize asymptotic convergence of bounded hybrid trajectories to weakly invariant sets. A detectability property is used to locate a set in which the Q-limit set of a trajectory is contained. Next, it is shown how the invariance principles can be used to certify asymptotic stability in hybrid systems. Lyapunov and Krasovskii theorems for hybrid systems are included.