A semi-algebraic approach for asymptotic stability analysis |
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Authors: | Zhikun She Bican Xia Rong Xiao Zhiming Zheng |
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Affiliation: | aLMIB and School of Science, Beihang University, China;bSchool of Mathematical Sciences, Peking University, China |
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Abstract: | 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. |
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Keywords: | Autonomous systems Asymptotic stability Lyapunov functions Quadratic form Semi-algebraic systems |
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