Stability for a class of homogeneous hybrid systems by annular Lyapunov analysis

For a class of homogeneous hybrid systems we present a set of annular Lyapunov-like conditions for inferring global pre-asymptotic stability of systems. Then, we prove that such conditions are mild, namely, that each globally pre-asymptotically stable system must satisfy them. Based on these results, we design a sum of squares algorithm that constructs a suitable Lyapunov-like function to fulfill such annular conditions. Finally, based on recent results on homogeneous approximations of hybrid systems, we point out that such conditions can also be used to deduce local pre-asymptotic stability for a wider class of hybrid systems.