Instability and overshoots of solutions for a class of homogeneous hybrid systems by Lyapunov-like analysis

For a class of homogeneous hybrid systems we present a generalization to the hybrid systems framework of Chetaev´s theorem and we propose a set of Lyapunov-like conditions for studying instability of the point x_e = 0 and overshoots of solutions (namely when the norm of the solution vector x at some time instant exceeds the norm of the initial condition of x). Based on these results, we design a sum of squares algorithm that constructs a suitable Lyapunov-like function to fulfill such conditions.