Robust tracking and disturbance rejection for systems with distributed time-delay

The robust servomechanism problem, which is to design a stabilizing controller such that the system output robustly tracks a given reference signal in the presence of certain disturbances, is considered for linear time-invariant time-delay systems of retarded type with distributed time-delay. The reference and the disturbance are assumed to satisfy a linear time-invariant delay-differential equation of retarded type with distributed time-delay. Necessary and sufficient conditions for the solvability of this problem are presented. The structure of the controller which solves this problem is also given. It is shown that the solution, when exists, involves two parts: (i) a servocompensator which mimics the dynamics of the reference and the disturbance; and (ii) a stabilizing compensator which asymptotically stabilizes the system obtained by augmenting the servocompensator to the plant.