Pole-zero cancellations and closed-loop properties of an H ∞ mixed sensitivity design problem

An H^∞ mixed sensitivity design problem is examined in order to gain an understanding of the phenomenon of closed-loop pole-zero cancellation and of the closed-loop properties resulting from an H^∞ design. A particular weighting-function construction is given that allows the designer freedom to exploit/prevent pole-zero cancellation and acts as a mechanism for (partial) pole placement. It is also shown that the normalized coprime factor design procedure of D. McFarlane and K. Glover (1989) can, for a particular class of plant, result in some (possibly undesirable) closed-loop pole-zero cancellations. This is illustrated with a simple design example. The results are presented in the scalar case for simplicity