Doyle et al. (1992) presented an algorithm 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 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.
IEEE Transactions on Automatic Control
Algorithm design and analysis, Chaos, Analytic positive, interpolation, phase margin optimization, strict Schur
Abdallah, Chaouki T.; Peter Dorato; and Domenico Famularo. "Analytic phase margin design." IEEE Transactions on Automatic Control 44, 10 (1999): 1894-1900. doi:10.1109/9.793731.