Exponential Stabilization for Timoshenko Beam with Distributed Delay in the Boundary Control

Abstract

We consider the exponential stabilization for Timoshenko beam with distributed delay in the boundary control. Suppose that the controller outputs are of the form α1u1(t)+β1u1(t-τ)+∫-τ0‍g1(η)u1(t+η)dη and α2u2(t)+β2u2(t-τ)+∫-τ0‍g2(η)u2(t+η)dη; where u1(t) and u2(t) are the inputs of boundary controllers. In the past, most stabilization results for wave equations and Euler-Bernoulli beam with delay are required αi>βi>0,i=1,2. In the present paper, we will give the exponential stabilization about Timoshenko beam with distributed delay and demand to satisfy the lesser conditions for αi,βi,i=1,2.