Stability analysis of Euler‐Bernoulli beam with input delay in the boundary control |
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Authors: | Ying Feng Shang Gen Qi Xu Yun Lan Chen |
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Affiliation: | Department of Mathematics, Tianjin University, Tianjin 300072, China |
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Abstract: | In this paper, we investigate an Euler‐Bernoulli system with input delay in the boundary control. Suppose that there is no delay in observation, y(t), of the system, and a partial input delay in the boundary control. The collocated boundary feedback control law u(t) = αy(t) + βy(t ? τ) is applied to obtain the closed loop system. By spectral analysis and Lyapunov method, we show that: when α>|β|, the closed loop system is exponentially stable for any τ>0; when α<|β|, the system is unstable for any τ>0; when α = |β|, the system is asymptotically stable for almost all τ>0. Finally, we provide numerical simulations to show the spectral distribution for different values of α and β. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society |
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Keywords: | Euler‐Bernoulli beam input delay feedback control exponential stability |
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