论文标题
线性周期性差异方程的指数稳定性
Exponential stability of linear periodic difference-delay equations
论文作者
论文摘要
本文涉及线性周期性差延迟系统的稳定性，其中解决方案的时间$ t $是线性组合，具有其值的定期系数，其值有限许多延迟的速度$ t-τ_1，\ ldots，t-τ_n$。当系数具有Hölder-con-Coninul衍生物时，我们为此类系统的指数稳定性建立了必要且充分的条件，该衍生物概括了1970年代Henry和Hale恒定系数的差异延迟系统获得的一个。该条件可以解释为相关线性控制系统的（操作员）谐波传递函数的半平面分析性。
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.
