A semi-algebraic approach for asymptotic stability analysis.

*(English)*Zbl 1217.93153Summary: 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.

##### Keywords:

autonomous systems; asymptotic stability; Lyapunov functions; quadratic form; semi-algebraic systems
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\textit{Z. She} et al., Nonlinear Anal., Hybrid Syst. 3, No. 4, 588--596 (2009; Zbl 1217.93153)

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