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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作者简介：孟琳，女，汉族，山东淄博人，现就读于北京航空航天大学系统与科学学院，2011级学生，硕士研究生在读，方向为动力系统；本科就读于北京科技大学数理学院，信息与计算科学专业。