Exponential stabilization of Timoshenko beam with input and output delays

Xiu-Fang  Liu; Gen-Qi Xu

doi:10.3934/mcrf.2016004

Article Contents

2016, Volume 6, Issue 2: 271-292. Doi: 10.3934/mcrf.2016004

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Exponential stabilization of Timoshenko beam with input and output delays

Xiu-Fang Liu^1, and
Gen-Qi Xu^2,

1.
School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072
2.
Department of Mathematics, Tianjin University, Tianjin 300072

Received: October 2014

Revised: October 2015

Published: June 2016

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Abstract

In this paper, we consider the exponential stabilization issue of Timoshenko beam with input and output delays. By using the Luenberger observer and Smith predictor we obtain an estimate of the state of the system, and by the partial state predictor we transform the delayed system into a without delay system, and then by the collocated feedback of the without delay system to obtain the control signal. We prove that under the control signal, the Timoshenko beam with output and input delays can be stabilized exponentially.

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Mathematics Subject Classification: 93C20, 93B52, 93D15, 93D25.

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