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A semi-algebraic approach for asymptotic stability analysis. (English) Zbl 1217.93153
Summary: 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. Experimental results show that our semi-algebraic approach is more efficient in practice, especially for low-order systems.

MSC:
93D20 Asymptotic stability in control theory
93B25 Algebraic methods
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