| 引用本文: | 刘和涛.一类时滞微分系统无条件稳定的代数判定[J].控制理论与应用,1986,3(1):106~110.[点击复制] |
| Liu Hetao.THE ALGEBRAIC CRITERION FOR UNCONDITIONAL STABILITY FOR A CLASS OF DIFFERENTIAL SYSTEMS WITH TIME DELAY[J].Control Theory and Technology,1986,3(1):106~110.[点击复制] |
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| 一类时滞微分系统无条件稳定的代数判定 |
| THE ALGEBRAIC CRITERION FOR UNCONDITIONAL STABILITY FOR A CLASS OF DIFFERENTIAL SYSTEMS WITH TIME DELAY |
| 摘要点击 718 全文点击 443 投稿时间：1984-03-28 修订日期：1985-12-07 |
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| DOI编号 |
| 1986,3(1):106-110 |
| 中文关键词 |
| 英文关键词 |
| 基金项目 |
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| 中文摘要 |
| 考虑定常的时滞微分系统
（*） x?（t）=Ax（t）+Bx（t-τ），τ≥0，A，B为常数矩阵。
如果对任何实数τ≥0，系统（*）的零解均为渐近稳定，则称系统（*）为无条件稳定。（*）为无条件稳定的代数判定问题由A.A.AНЛPHOB[1]于1946年提出。对于A、B为2X2矩阵的情形，文[2，3，4]考虑了这类问题，但所得形式不够明显或条件不够完整。1984年文[5]对此问题给出了结论。本文给出反例以说明文[5]定理4.1所给的代数判定条件不是必要的。我们在此给出了A、B为2X2矩阵时的代数判定，它被归结为四次实系数方程无正根的代数判定。 |
| 英文摘要 |
| The problem about the algebraic criterion for unconditional stability with respect to all delay τ for the following system
x?（t）=Ax（t）+Bx（t-τ），τ≥0，A，B are constant matrices.
Has been proposed by A.A.AНЛPHOB[1] in 1946. In case A, B has are 2X2 matrices [2，3，4] have considered this problem, but the results they have given are not evident and not complete. [5] has given a result recently (1984). In this Paper we give a counter example to show that the result given in [5] is incorrect, that is, problem to a algebraic criterion of the nonexistence of positive roots of a fourth order equation with real coefficients, in this way, we give the corresponding result for the case where A, B are 2X2 matrices. |
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