An example for the switching delay feedback stabilization of an infinite dimensional system: The boundary stabilization of a string
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 …
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 …
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