Results on finite time stability for a class of hybrid systems

This paper introduces notions and tools for finite time stability of closed sets for a class of hybrid systems. The proposed finite time stability notion consists of both Lyapunov stability and finite time convergence. Several sufficient conditions for a closed set to have such a property for a hybrid system are established. Robustness of finite time stability to small perturbations is studied by the regularity of the system data. Relationships between finite time stability and asymptotic stability of sets are also investigated. Examples illustrating the results are discussed throughout the paper