Rapid stabilisation of an Euler–Bernoulli beam with the internal delay control

Abstract

In this paper, we are concerned with rapid stabilisation of an Euler--Bernoulli beam with internal delayed control. Herein we introduce a new approach of the feedback control design from the system equivalence point of view. The design approach can be divided into several steps. First, we construct a target system of the desired stability. Second, we select a suitable integral transform that transforms the present system to the target system. In this procedure, one can get a corresponding feedback control. Third, we find a transform that transforms the target system to the present system, which provides the equivalence of both systems. Finally, we prove that the two transforms are bounded linear operators in an appropriate Hilbert space.