Mathematics Commons^™

Lack Of Time-Delay Robustness For Stabilization Of A Structural Acoustics Model, George Avalos, Irena Lasiecka, Richard Rebarber

Department of Mathematics: Faculty Publications

In this paper we consider a natural robustness question for a model for structural acoustics. This model, which has been of great interest in recent years, is represented by a wave equation in R^2 coupled to a Kelvin--Voigt beam; the coupling is natural physically, and is represented mathematically by highly unbounded operators. We assume that the observation consists of point evaluation of the beam position, the beam velocity, and the wave velocity. We are interested in the effect of arbitrarily small delays in the feedback loop on a controller that uses these observations. We show that it is not possible …