In 5, algorithms are presented for analytic gain and phase margin design. Without special care however, the compensator computed with this algorithm is not a real rational function. In 3, it is shown that with some care, a real rational compensator for phase margin design can be computed from the theory in 5. In this paper both gain and phase margin problems are reduced to interpolation problems with positive-real functions, which saves a step in the algorithm shown in 5, where interpolation is done with bounded-real functions, in the case of gain margin design.
Atti della 6th IEEE Mediterranean Conference on Control and Systems
Abdallah, Chaouki T.; D. Famularo; and Peter Dorato. "Analytic Gain and Phase Margin Design." Atti della 6th IEEE Mediterranean Conference on Control and Systems (1998): 1-6. https://digitalrepository.unm.edu/ece_fsp/59