论文标题
延迟差异方程的多重性诱导的延迟类型方程
Multiplicity-induced-dominancy for delay-differential equations of retarded type
论文作者
论文摘要
线性时间延迟系统持续兴趣的一个重要问题是提供有关其参数的条件，以确保解决方案的指数稳定性。最近的作品探索了光谱技术，以表明，对于某些低阶延迟差异方程，延迟类型的差异方程，最大多重性的光谱值是主导的，因此确定了系统的渐近行为，该系统（一种称为多重性诱导的占主导地位）的属性。这项工作进一步探讨了这种属性，并显示了其对延迟类型的任意顺序的一般线性延迟分化方程的有效性，包括系统表示的单个延迟。更确切地说，利用了具有最大多重性的真实词的特征函数与Kummer汇合的超几何函数之间的有趣联系。我们还提供了说明我们主要结果的示例。
An important question of ongoing interest for linear time-delay systems is to provide conditions on its parameters guaranteeing exponential stability of solutions. Recent works have explored spectral techniques to show that, for some low-order delay-differential equations of retarded type, spectral values of maximal multiplicity are dominant, and hence determine the asymptotic behavior of the system, a property known as multiplicity-induced-dominancy. This work further explores such a property and shows its validity for general linear delay-differential equations of retarded type of arbitrary order including a single delay in the system's representation. More precisely, an interesting link between characteristic functions with a real root of maximal multiplicity and Kummer's confluent hypergeometric functions is exploited. We also provide examples illustrating our main result.
