School of Mathematics and Systems Science, Beijing University of Aeronautics and       Astronautics, Beijing, 100191, China. Contact person: Meng Lin,

Abstract: We in this paper provide a real root classification based approach for asymptotic stability analysis of uncertain polynomial dynamical systems. We start from linearizing an uncertain polynomial dynamical system and then formulate the asymptotic stability problem of its equilibria as a semi-algebraic system, which consists of the equilibrium equations, the Lyapunov equation and certain inequalities used for checking the positive-definiteness of a matrix. Afterward, with real root classification, we obtain a sufficient condition, which is a set of analytic inequalities on the parameters, for the system to have the prescribed number of asymptotically stable equilibria. Finally, some experimental examples are used to demonstrate the feasibility of this approach.
Key words: asymptotic stability; Lyapunov equation; semi-algebraic systems; real root classification

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作者簡介：孟琳，女，漢族，山東淄博人，現就讀于北京航空航天大學系統與科學學院，2011級學生，碩士研究生在讀，方向為動力系統；本科就讀于北京科技大學數理學院，信息與計算科學專業。