On finite gain Lp stability for hybrid systems

We characterize finite gain Lp stability properties for hybrid dynamical systems. By defining a suitable concept of hybrid Lp norm, we provide sufficient Lyapunov conditions for Lp stability of hybrid dynamics, which cover the well known continuous-time and discrete-time Lp stability notions as special cases. We also focus on homogeneous dynamics and prove a result stating the equivalence among Lp stability, ISS, global exponential stability and local asymptotic stability of the hybrid system with no inputs. Finally, we provide some input-output results and an LMI based L2 gain estimate for a class of homogeneous hybrid systems.