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        Dynamic Feedback Stabilization for Timoshenko Beam with Locally Input Controls and Input Distributed Delay

        2021-10-20 03:26:34WANGXiaorui王小瑞LIUXilan劉喜蘭
        應(yīng)用數(shù)學(xué) 2021年4期

        WANG Xiaorui(王小瑞),LIU Xilan(劉喜蘭)

        ( 1.School of Mathematics and Statistics,Qinghai Nationalities University,Xining 810007,China;2.School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,China)

        Abstract:In this paper,based on the method of dynamic feedback controller treating the boundary control with delays,we consider the exponential stabilization for a Timoshenko beam with interior locally input delayed controls and input distributed delay control.We design a new dynamic feedback control law to stabilize exponentially this system,and show that the original system is stabilized exponentially.

        Key words:Timoshenko beam;Input distributed delay;Dynamic feedback controller;Exponential stabilization

        1.Introduction

        2.Design of Dynamic Feedback Controller

        3.Representation of the System(2.2)

        4.The Proof of Theorem 2.1

        5.The Proof of Theorem 2.2

        6.Conclusion

        In this paper,we design a dynamic feedback controller to treat the stabilization of Timoshenko beam with locally input controls and input distributed delay.Under this control strategy,we prove that the closed-loop system(2.8)is exponentially stable for any time delayτ >0 by verifying the exponential stability of the system(2.7)on the some certain conditions.We mainly use the exact observability of the dual system in finite time to verify the exponential stabilization of closed-loop system.The approach proposed in this paper can be applied to more complicated models theoretically.

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