Analytic phase margin design

In [4] an algorithm is presented for analytic phase margin control design. Without special care, however, the compensator computed with this algorithm may not be a real rational function. The problem is evident when the plant has real unstable poles. In this case the algorithm in [4] requires a mapping of real points into complex values, and it is not clear that the resulting compensator has real coefficients. The purpose of this paper is to show how a complex mapping required in this algorithm can always be selected so that the compensator does have real coefficients.