Relaxed Persistent Flow/Jump Conditions for Uniform Global Asymptotic Stability

For hybrid systems, sufficient conditions are derived for the uniform global asymptotic stability of a given closed set. These conditions are written in terms of a Lyapunov function candidate and assume a semiglobal practical persistent flow (resp. persistent jump) property of the solutions to the hybrid system. The use of the new conditions is illustrated via the stability analysis of a physically inspired example and of an event-triggered control algorithm.