时滞对一类线性时滞系统收敛速度的正影响
On the Positive Effect of Delay on the Rate of Convergence of a Class of Linear Time-Delayed Systems
摘要：
本文是一个长期观察到的现象增加的稳定裕度，从而收敛速度的一类线性系统，由于时间延迟的综合研究。我们使用Lambert W函数来确定（a）在什么系统中延迟可以导致收敛速度的增加，（b）收敛速度大于无延迟系统的收敛速度的时间延迟的确切范围，以及（c）导致最大收敛速度的延迟值的估计。对于系统矩阵特征值均为负实数的特殊情况，我们将结果扩展到时滞存在时的收敛速度仅取决于具有最小和最大实部的特征值.此外，我们确定的最大收敛速度和相应的最大化时间延迟的精确值。通过一个数值例子，我们证明了我们的结果在实际应用中加速协议算法的网络系统使用延迟反馈。
英文摘要：
This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems the delay can lead to increase in the rate of convergence, (b) the exact range of time delay for which the rate of convergence is greater than that of the delay free system, and (c) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked~systems by use of a delayed feedback.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
