Z. She, R. Yan, B. Xue, and Z. Zheng (PRC)
Asymptotic stability, Lyapunov functions, semialgebraic systems, quantifier elimination.
In this paper, we analyze the asymptotic stability of autonomous and non-autonomous differential systems by verifying the existence of Lyapunov functions. We start with an algebraic approach for verifying the existence of a Lyapunov function in quadratic form for autonomous systems by first formulating a semi-algebraic system and then solving such a semi-algebraic system by a semi-algebraic system solver. Then, this algebraic approach is extended to parametric autonomous systems and (parametric) non-autonomous systems by introducing quantifiers during algebraization. Experiments on some examples in the literature show the success of our approach in practice.
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