Journal
SYSTEMS & CONTROL LETTERS
Volume 60, Issue 4, Pages 226-233Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2011.01.004
Keywords
Hyperbolic pde; Feedback stabilization of pdes; Delay; Boundary feedback; Switching delay; Wave equation; String; Feedback with delay; Past observation
Funding
- DAAD [D/0811409]
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For vibrating systems, a delay in the application of a feedback control may destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end. We show that certain delays in the boundary feedback preserve the exponential stability of the system. In particular, we show that the system is exponentially stable with delays freely switching between the values 4L/c and 8L/c, where L is the length of the string and c is the wave speed. (C) 2011 Elsevier B.V. All rights reserved.
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