Some second-order vibrating systems cannot tolerate small timedelays in their damping

摘要

The purpose of this work is to show that the finite-dimensionalnproperty of robustness with respect to small time delays does not holdnfor a general class of infinite-dimensional systems of a certain form.nThe abstract systems considered encompass many well-known types ofndamped hyperbolic partial differential equations whose damping operatornis represented by a symmetric operator B such that An^-1/2BA^-1/2 is a compact operator in ansuitable Hilbert space. It is shown that the abstract systems are notnrobust with respect to almost arbitrary time delays in the damping