线性周期差分延迟方程的指数稳定性
Exponential stability of linear periodic difference-delay equations
AI总结：
本文提出了一种线性周期差分延迟系统指数稳定性的判定条件，扩展了常系数系统的结果，并通过解析性条件解释了其数学意义。
摘要：
本文研究了线性周期差分延迟系统的稳定性，其中解在时间t处的值是其在有限多个延迟时刻t-τ₁,…,t-τ_N处的值的线性组合，具有周期系数。我们建立了当系数具有Hölder连续导数时，此类系统指数稳定性的必要且充分条件，该条件扩展了Henry和Hale在1970年代为常系数差分延迟系统所获得的条件。该条件可被理解为一个相关线性控制系统关联的（算子值）谐波传递函数在半平面中的解析性。
英文摘要：
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants $t-τ_1,\ldots,t-τ_N$. We establish a necessary and sufficient condition for exponential stability of such systems when the coefficients have Hölder-continuous derivative, that generalizes the one obtained for difference delay systems with constant coefficients by Henry and Hale in the 1970s. This condition may be construed as analyticity, in a half plane, of the (operator valued) harmonic transfer function of an associated linear control system.
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。
