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http://hdl.handle.net/10397/7029
| 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 |
| Appears in Collections: | Journal/Magazine Article |
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| Xu_Wave_Boundary_Control.pdf | 216.55 kB | Adobe PDF | View/Open |
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