记笔记

An Algorithm to Verify a Class of Matrix Inequalities in the Global Stability of Nonlinear Systems

Huiling GU¹Yimin SUN²

1. School of Mathematics,Sun Yat-sen University 2. Guangdong Province Key Laboratory of Computational Science,School of Mathematics,Sun Yat-sen University

摘要：The global stability and stabilization for nonlinear systems is a challenging problem in control theory.The conditions like R（t）≤-∈_OI or R（x） ≤-∈₀ I often appeared in many related literature.Obviously,to verify this condition is not easy,partly because there is not a general method to find the precise value of its roots by radicals for a univariate polynomial with degree more than 4.In this paper,we mainly discuss the case which all entries in 91 are polynomials and give a feasible algorithm to verify the condition R（t）≤-∈₀ I or R（x）≤-∈₀ I.The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on real algebraic geometry and mathematics mechanization method.Finally,the authors will give some examples to show the application of our results.

关键词：

Global stability; polynomial; complete discrimination system; mathematics mechanization;

基金：

supported by Guangdong Natu-ral Science Foundation No.2019A1515011804； Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University（2020B1212060032）；

会议名称：

第41届中国控制会议

会议时间：

2022-07-25

会议地点：

中国安徽合肥