Stabilization of an Euler-Bernoulli beam with boundary input delay

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.