Stabilisation of Timoshenko beam system with delay in the boundary control

Abstract

In this paper, we consider the exponential stabilisation problem of a Timoshenko beam with delay in boundary control. Suppose that the controller outputs of the forms α1u1(t) + β1u1(t − τ) and α2u2(t) + β2u2(t − τ) where u1(t) and u2(t) are the inputs of boundary controllers. In the past, most of the stabilisation results are required αj > βj > 0, j = 1, 2. In the present paper, we shall give a new dynamic feedback control law that makes the system exponential stabilisation ∀τ > 0 provided that |αj| ≠ |βj|(j = 1, 2). The exponential stabilisation result is proved via test of exact observability of the system.