International Journal of Control, Vol.86, No.6, 1165-1178, 2013
Stabilisation of Timoshenko beam system with delay in the boundary control
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 (1)u(1)(t) + (1)u(1)(t ) and (2)u(2)(t) + (2)u(2)(t ) where u(1)(t) and u(2)(t) are the inputs of boundary controllers. In the past, most of the stabilisation results are required (j) > (j) > 0, j = 1, 2. In the present paper, we shall give a new dynamic feedback control law that makes the system exponential stabilisation ? > 0 provided that |(j)| |(j)|(j = 1, 2). The exponential stabilisation result is proved via test of exact observability of the system.