Robust tracking and disturbance rejection for time-delay systems

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 discrete delays. The reference and the disturbance are assumed to satisfy a constant-coefficient linear delay-differential equation of retarded type with discrete delays. 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 necessary and sufficient conditions are exactly the counterparts of the conditions for delay-free systems. Furthermore, as in the case of delay-free systems, the solution 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. An example is also presented to illustrate the design approach.