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应用科学学报

• 信号与信息处理 • 上一篇    

时滞偏微分方程系统的稳定性检验

肖扬 1, KIM Kiseon 2   

  1. 1. 北京交通大学 信息科学研究所，北京 100044; 2. 光州理工学院 信息与通信工程系，光州 500-712
  • 收稿日期:2008-05-04 修回日期:2008-08-19 出版日期:2008-12-10 发布日期:2008-12-10
  • 通信作者: 肖扬

Stability Test for Time-Delay Partial Differential Equation Systems

XIAO Yang 1, KIM Kiseon 2   

  1. 1. Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China; 2. Department of Information and Communications, Gwangju Institute of Science and Technology, Gwangju 500-712, Korea
  • Received:2008-05-04 Revised:2008-08-19 Online:2008-12-10 Published:2008-12-10
  • Contact: XIAO Yang

被引次数

3

摘要： TDPDE系统的稳定性涉及到2D拟多项式, TDPDE系统的特征多项式为2D拟多项式，而其零点为一些连续的超曲面, 不再是孤立的和可分离的. 这导致检验TDPDE系统的稳定性非常困难. 为解决上述问题，提出一种检验TDPDE系统渐近稳定性的方法，该方法通过检验TDPDE系统对应的2D特征多项式的Hurwitz稳定性来确定TDPDE系统的渐近稳定性. 本文提出的定理建立了TDPDE系统的渐近稳定性与对应的2D特征多项式的Hurwitz稳定性关系, 提供了2D特征多项式(2D拟多项式)的Hurwitz稳定性检验方法. 由该文结果导出具有简单检验过程的2D拟多项式的Hurwitz-Schur稳定性数值检验算法，并用实例说明其应用。

关键词: 时滞偏微分方程系统, Hurwitz-Schur稳定性, 2D拟多项式, 检验算法

Abstract: Stability of time-delay partial differential equations (TDPDE) systems involves 2D quasi-polynomials, while zeros of the characteristic polynomials (2D quasi-polynomials) of TDPDE systems are some continuous and hyper curved surfaces. Zeros are not isolated and separated, leading to difficulty in the stability test of TDPDE systems. To solve the problem, this paper proposes an approach to test asymptotic stability of TDPDE systems by a Hurwitz stability test of 2D characteristic polynomials of the systems. The proposed theorems establish the relationship between the asymptotic stability of TDPDE systems and the Hurwitz stability test of 2D characteristic polynomials, and provide a test approach of the Hurwitz stability test of 2D characteristic polynomials (2D quasi-polynomials). Base on the results, a numerical algorithm with a simpler test procedure for Hurwitz-Schur stability test of 2D quasi-polynomials is developed. An example illustrates the application of the proposed approach.

Key words: time-delay partial differential equation systems, Hurwitz-Schur stability, 2D quasi-polynomials, test algorithm

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