引用本文:胡跃明.线性多时滞差分微分系统全时滞稳定的代数判据[J].控制理论与应用,1987,4(3):40~47.[点击复制]
Hu Yueming.ALGEBRAIC CRITERIAS OF STABILITY FOR ALL DELAYS IN LINEAR DIFFERENTIAL-DIFFERENCE SYSTEM WITH MULTIPLE DELAYS[J].Control Theory and Technology,1987,4(3):40~47.[点击复制]
线性多时滞差分微分系统全时滞稳定的代数判据
ALGEBRAIC CRITERIAS OF STABILITY FOR ALL DELAYS IN LINEAR DIFFERENTIAL-DIFFERENCE SYSTEM WITH MULTIPLE DELAYS
摘要点击 1132  全文点击 559  投稿时间:1985-11-11  修订日期:1986-03-07
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DOI编号  
  1987,4(3):40-47
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英文关键词  
基金项目  
作者单位
胡跃明 安徽经济管理学院 
中文摘要
      考虑下列线性多时滞差分微分系统 x’(t) = A0x(t) + ∑Akx(t – Tk*r) (1) 其中x∈Rn,Ak(k=0, 1, …, N)是n*n常数矩阵;Tk=(Tk1, Tk2, …, TkM),Tkj(k=1, …, N; j=1, …, M)是整数,rT=(r1, r2, …, rM),Tk*r=∑Tkj*rj。本文利用Lyapunov函数和Lyapunov泛函,给出了系统(1)全时滞稳定的代数条件,克服了Hale文中验证“超越”条件的困难,为实际工作者提供了十分有效而方便的判别方法。
英文摘要
      In this paper, the author discusses the following linear differential-difference systems; x’(t) = A0x(t) + ∑Akx(t – Tk*r) (1) Where x∈Rn,Ak(k=0, 1, …, N) are constant matrices, Tk=(Tk1, Tk2, …, TkM),Tkj(k=1, …, N; j=1, …, M) are nonnegative integers, rT=(r1, r2, …, rM),Tk*r=∑Tkj*rj, some algebraic criteria of stability for all delays of system (1) are given by using Lyapunov’s direct method. These results are very useful in real applications.