Stability analysis is one of the most important problems in analysis of hybrid dynamical systems. In this paper, a computational method of Lyapunov functions is proposed for stability analysis of hybrid automata that have set-valued vector fields. For this purpose, a formulation of matrix-valued sums of squares is provided and applied to derive an LMI/LME problem whose solution yields a Lyapunov function.

This paper provides a computational method to construct a Lyapunov function to prove a stability of hybrid automata that can have nonlinear vector fields. Algebraic inequalities and equations are formulated, which are solved via LMI optimization. Numerical examples are presented to illustrate the proposed method.