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

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