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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 xe = 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.