文章摘要
刘兴文.时滞系统稳定性分析--齐次多项式Lyapunov泛函方法[J].西南民族大学自然科学版,2018,44(1):75-82
时滞系统稳定性分析--齐次多项式Lyapunov泛函方法
Homogeneous polynomial Lyapunov functional for stability analysis of systems with delays
投稿时间:2018-01-09  修订日期:2018-01-09
中文关键词: 时滞, 齐次多项式Lyapunov泛函, Kronecker积, 稳定性.
英文关键词: delay  homogeneous polynomial Lyapunov functional  Kronecker product  stability
基金项目:国家自然科学基金(61673016, 61703353);中央高校基本科研业务费专项基金项目青年教师基金项目(12NZYQN17); 四川省教育厅创新团队(15TD0050);四川省科技厅青年科技创新团队 (2017TD0028).
作者单位E-mail
刘兴文 西南民族大学 459520603@qq.com 
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中文摘要:
      研究时变时滞线性系统的稳定性. 二次Lyapunov泛函是分析这类系统稳定性的有力工具, 但往往难以给出低保守性稳定性条件. 为克服这个困难提出了齐次多项式Lyapunov泛函方法, 建立了时滞系统的渐近稳定条件. 传统的二次Lyapunov泛函是所用泛函的特例. 数值例子表明所用方法有效, 特别是时滞导数上界较大时, 本方法效果显著, 具有十分明显的低保守性优势.
英文摘要:
      This paper addresses the stability problem of dynamic systems with time-varying delays. For this class of systems, quadratic Lyapunov functional is the most popular and powerful tool for stability analysis, and usually results in stability conditions with high conservativeness. In order to overcome the drawback, this paper tries to propose a new type of Lyapunov functional-homogeneous polynomial Lyapunov functional, based on which an asymptotic stability criterion is established. A numerical example shows that the presented method is effective, especially when the upper bounds of derivative of delays are relatively large.
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