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 and ; where and are the inputs of boundary controllers. In the past, most stabilization results for wave equations and Euler-Bernoulli beam with delay are required . In the present paper, we will give the exponential stabilization about Timoshenko beam with distributed delay and demand to satisfy the lesser conditions for .
Highlights
Since the extensive applications of Timoshenko beam in high-Tech, the stabilization problem has been a hot topic in the mathematical control theory and engineering; for instance, see [1,2,3,4,5] and the references therein
We designed a new controller for a Timoshenko beam with distributed delay in the boundary that stabilizes exponentially the system
We need to study the corresponding control strategy for the data-driven system
Summary
Since the extensive applications of Timoshenko beam in high-Tech, the stabilization problem has been a hot topic in the mathematical control theory and engineering; for instance, see [1,2,3,4,5] and the references therein. Xu et al (see [6]) studied firstly stabilization of the 1-d wave systems with delay of the form αu(t) + βu(t − τ) They proved that the system with control delay is exponential stable if α > β > 0 and unstable if β > α. Xu and Wang in [13] discussed the Timoshenko beam with boundary control delay, and they stabilized the system by a dynamic feedback controller. We still consider Timoshenko beam with boundary control distributed delay. We will seek for a dynamic feedback control law that exponentially stabilizes the Timoshenko beam with distributed delay under certain conditions.
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