An example for the switching delay feedback stabilization of an infinite dimensional system: The boundary stabilization of a string - Gugat, Martin; Tucsnak, Marius (Systems & Control Letters, 2011)
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 4Lc and 8Lc, where L is the length of the string and c is the wave speed. © 2011 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2011.nat.dma.zentr.anexam
Keywords: Boundary feedback; Delay; Feedback stabilization of pdes; Feedback with delay; Hyperbolic pde; Past observation; String; Switching delay; Wave equation