Discovering Polynomial Lyapunov Functions for Continuous Dynamical Systems

摘要：

In this paper we analyze asymptotic stability of polynomial dynamical systems by discovering Lyapunov functions beyond quadratic forms. We first derive an algebraizable sufficient condition for the existence of a polynomial Lyapunov function. Then we apply a real root classification based method step by step to formulate this derived condition as a semi-algebraic set such that the semialgebraic set only involves the coefficients of the pre-assumed polynomial. Finally, we compute a sample point in the resulting semi-algebraic set for the coefficients resulting in a Lyapunov function. An example is used to illustrate the prototypical implementation of our algorithm.

作者: Zhikun She Haoyang Li Bai Xue

作者单位: SKLSDE, LMIB and School of Mathematics and Systems Science Beihang University, Beijing, China School of Mathematics and Systems Science, Beihang University, Beijing, China

会议类型: 国际会议

会议名称: The Fourth International Conference on Mathematical Aspects of Computer and Information Sciences(第四届计算机与信息科学中的数学方法国际会议 MACIS 2011)

会议地点: 北京

会议语种:英文

页码: 216-225

在线出版日期: 2011-10-21（万方平台首次上网日期，不代表论文的发表时间）