Nonrobustness of feedback systems under large perturbations in time delays

Changes in the spectrum of a linear system with countably many delays, in the case when some of the delays grow to infinity, are investigated. It is shown that some eigenvalues must either cross or at least approach the imaginary axis and, moreover, for any neighborhood of a point on the imaginary axis there is an eigenvalue in this neighborhood if delays are sufficiently large. These results are formulated for a general class of systems involving countably many delays. The theoretical results obtained explain the well-known practical observations that closed-loop systems lose robustness if a time delay in the feedback loop becomes too large