Sensitivity Reduction by Stable Controllers for MIMO Infinite Dimensional Systems via the Tangential Nevanlinna-Pick Interpolation

We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in C̅₊, but they are allowed to possess infinitely many poles in C₊. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method.