A semi-algebraic approach for asymptotic stability analysis

This paper deals with the problem of computing Lyapunov functions for asymptotic stability analysis of autonomous polynomial systems of differential equations. We propose a new semi-algebraic approach by making advantage of the local property of the Lyapunov function as well as its derivative. This is done by first constructing a semi-algebraic system and then solving this semi-algebraic system in an adaptive way. Experiment results show that our semi-algebraic approach is more efficient in practice, especially for low-order systems.