On the Coalescence of Spectral Values and its Effect on the Stability of Time-delay Systems: Application to Active Vibration Control

Abstract

For linear delay-differential equations, a question of ongoing interest is to determine conditions on the equation parameters that guarantee exponential stability of solutions. Recent results have shown an unexpected link between the stable manifold and the variety characterizing multiple characteristic spectral values allowing to the right-most root assignment. In this paper, such an idea is presented and exploited in the control of active vibrations.