In this paper, we introduce a new kind of feedback controller for an Euler-Bernoulli beam with boundary delayed control. Different from the approach of the Smith predictor and dynamic feedback control, the new feedback controller is of the integral form in spatial variable, that is called the integral-type full state feedback controller. Our goal of the present paper is to show that one can select appropriate kernel functions such that the closed-loop system is exponentially stable. Here we mainly give an approach of selecting kernel functions. To prove the stability of the closed-loop system, we construct a bounded and revertible linear transformation that establishes the equivalence between a stable target system and the controlled system.

中文翻译：

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具有边界输入延迟的欧拉-伯努利光束的稳定性

在本文中，我们介绍了一种具有边界延迟控制的 Euler-Bernoulli 梁的新型反馈控制器。不同于Smith预测器和动态反馈控制的方法，新的反馈控制器是空间变量的积分形式，称为积分型全状态反馈控制器。我们本文的目标是表明可以选择合适的核函数，使闭环系统呈指数稳定。这里我们主要给出一种选择核函数的方法。为了证明闭环系统的稳定性，我们构造了一个有界且可逆的线性变换，以建立稳定目标系统和受控系统之间的等价性。