Stabilization of an Euler-Bernoulli beam with input delay in the boundary control

In this paper, we consider a cantilever Euler-Bernoulli beam with controller delay. Suppose that the output of the boundary controller is of the form alpha u(t) + beta u(t-tau), where u(t) is the controller input. It is well known that a system with a collocated feedback control law is exponentially stable if beta = 0, and it is unstable with the same control law when alpha = 0. In the present paper, we shall design a dynamic controller that makes the system stabilize exponentially for any vertical bar alpha vertical bar not equal vertical bar beta vertical bar and tau > 0. Furthermore, we discuss the stability of the system for vertical bar alpha vertical bar = vertical bar beta vertical bar. (C) 2012 Elsevier B.V. All rights reserved.