| 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] |
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| 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 781 全文点击 420 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 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 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. |
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