Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/7029
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Title: Stabilization of wave systems with input delay in the boundary control
Authors: Xu, GQ
Yung, SP
Li, LK
Issue Date: Oct-2006
Source: ESAIM. Control, optimisation and calculus of variations, Oct. 2006, v. 12, no. 4, p. 770-785
Abstract: In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight (1 - μ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C₀ group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hubert space. Furthermore, we show that when the weight μ > 1/2, for any time delay, we can choose a suitable feedback gain so that the closed loop system is exponentially stable. When μ = 1/2 we show that the system is at most asymptotically stable. When μ < 1/2, the system is always unstable.
Keywords: Feedback control
Spectrum analysis
Stabilization
Vectors
Velocity control
Waves
Publisher: EDP Sciences
Journal: ESAIM. Control, optimisation and calculus of variations 
ISSN: 1292-8119
EISSN: 1262-3377
DOI: 10.1051/cocv:2006021
Rights: © EDP Sciences, SMAI 2006
The original publication is available at www.esaim-cocv.org
The following article "Gen Qi Xu, Siu Pang Yung and Leong Kwan Li (2006). Stabilization of wave systems with input delay in the boundary control. ESAIM: Control, Optimisation and Calculus of Variations, 12, pp 770-785. doi:10.1051/cocv:2006021." is available at http://www.esaim-cocv.org/action/displayAbstract?fromPage=online&aid=8133878
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