张海,蒋威.具变时滞的非线性退化微分系统的渐近稳定性判据[J].数学研究及应用,2010,30(4):664~674
具变时滞的非线性退化微分系统的渐近稳定性判据
Asymptotic Stability Criteria for Singular Differential Nonlinear Systems with Time-Varying Delays
投稿时间:2008-06-20  最后修改时间:2008-10-06
DOI:10.3770/j.issn:1000-341X.2010.04.011
中文关键词:  退化微分系统  变时滞  V泛函  渐近稳定性判据  矩阵方程  矩阵不等式.
英文关键词:singular differential systems  time-varying delays  V-functional  asymptotic stability criteria  matrix equations  matrix inequalities.
基金项目:国家自然科学基金(Grant No.10771001),教育部高校博士学科点专项科研基金(Grant No.20093401110001),安徽省教育厅自然科学研究重大项目(Grant No.KJ2010ZD02),安徽省教育厅自然科学研究项目(Grant Nos.KJ2008B152; KJ2009B098),安徽大学创新团队基金.
作者单位
张海 安徽大学数学科学学院, 安徽 合肥 230039; 安庆师范学院数学与计算科学学院, 安徽 安庆 246011 
蒋威 安徽大学数学科学学院, 安徽 合肥 230039 
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中文摘要:
      本文讨论具有多变时滞的非线性退化微分系统的渐近稳定性. 研究了一般退化时滞微分系统的$V$泛函方法, 基于$V$泛函方法和分析技巧给出了具有多变时滞的非线性退化微分系统的渐近稳定性判据, 稳定性判据被描述为矩阵等式或者矩阵不等式. 所得结果在计算上是可行的和有效的.
英文摘要:
      In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.
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