On the Algebraization of Asymptotic Stability Analysis for Differential Systems

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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