| 引用本文: | 秦元勋，俞元洪.一类时滞微分系统无条件稳定的条件[J].控制理论与应用,1984,1(1):23~35.[点击复制] |
| Qin Yuanxun ， Yu Yuanhong.UNCONDITIONAL STABILITY CONDITIONS FOR A CLASS OF DIFFERENTIAL SYSTEMS WITH TIME DELAY[J].Control Theory and Technology,1984,1(1):23~35.[点击复制] |
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| 一类时滞微分系统无条件稳定的条件 |
| UNCONDITIONAL STABILITY CONDITIONS FOR A CLASS OF DIFFERENTIAL SYSTEMS WITH TIME DELAY |
| 摘要点击 1299 全文点击 546 投稿时间：1983-05-06 修订日期：1983-06-29 |
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| DOI编号 |
| 1984,1(1):23-35 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 中文摘要 |
| 本文给出系统dx(t)/dt=a1x(t)+a2x(t-τ), dy(t)/dt=c1x(t)+c2x(t-τ)+d1y(t)+d2y(t-τ)对任意时滞τ≥0为无条件稳定的必要与充分条件。这个问题是 A.A AH POHOB1在1946年提出的，1960年文[2]给出了这个问题的初步结果。本人给出了这个结果的明显形式，它是在判定四次代数方程在区间[-1，1]内无实根的基础上得到的。为了工程技术人员的方便，我们也给出了这个判定的明显形式。 |
| 英文摘要 |
| In this paper, necessary and sufficient conditions for unconditional stability with respect to al delay τ for the following system
dx(t)/dt=a1x(t)+a2x(t-τ), dy(t)/dt=c1x(t)+c2x(t-τ) +d1y(t)+d2y(t-τ), are given. This problem was proposed by A.A AH POHOB1 in 1946. Preliminary results [2] were given by us in 1960, and are given in explicit forms in this paper. The results depend on the nonexistence of real roots of a fourth order algebraic equation within an interval [-1，1], and are given explicitly in order to facilitate their use by engineers. |
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