时滞积分微分Volterra方程的分析与控制
Analysis and control of integro-differential Volterra equations with delays
摘要：
本文的目的是介绍一个半群方法，在状态，控制和观测部分的时滞线性积分微分系统。一方面，我们利用积空间将状态时滞积分微分方程转化为一个标准Cauchy问题，然后利用扰动技术（反馈）证明了该问题的适定性，得到了一个新的常数变易公式以及一些谱性质。另一方面，我们利用所得结果证明了在Salamon-Weiss意义下，状态、控制和观测部分具有时滞的积分微分系统构成了分布无穷维正则线性系的一个子类.
英文摘要：
The purpose of this paper is to introduce a semigroup approach to linear integro-differential systems with delays in state, control and observation parts. On the one hand, we use product spaces to reformulate state-delay integro-differential equations to a standard Cauchy problem and then use a perturbation technique (feedback) to prove the well-posendess of the problem, a new variation of constants formula for the solution as well as some spectral properties. On the other hand, we use the obtained results to prove that integro-differential systems with delays in state, control and observation parts form a subclass of distributed infinite-dimensional regular linear systems in the Salamon-Weiss sense.
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