Sensitivity shaping for systems with time delay by Nevanlinna-Pick interpolation

It was pointed out by Foias, Tannenbaum and Zames that the unweighted H_infin sensitivity optimization for systems with time delay can be formulated as a finite dimensional Nevanlinna-Pick interpolation. The purpose of this paper is to consider this formulation. The synthesis of the controller and the shaping of sensitivity function are carried out by the theory of Nevanlinna-Pick interpolation with degree constraint. It turns out that the controller has a structure of the Smith predictor. The finite impulse response system is only determined by non-minimum phase zeros and unstable poles of the plant.