Stability and control of feedback systems with time delays

Feedback systems are important in applications, for example, optical feedback lasers, phase-locked frequency synthesizers and wave equations with feedback stabilization at the boundary, and the problem regarding sensitivity and robustness of the feedback system with respect to time delays has attracted a lot of attention. In this paper we continue the discussion on sensitivity and robustness of the feedback stabilization of neutral differential delay equations with respect to variation in the delays and with respect to a time delay in the feedback loop. Our main result shows that robustness of the stabilization actually depends on the radius of the essential spectrum of the semigroup associated with the equation.