A Class of Convex Optimal km-synthesis Problems

A class of optimal km-synthesis problems involving rank one plants is considered, where km is the Multivariable Stability Margin for systems with complex diagonally-structured uncertainty. For this class, the optimal km-synthesis problem is convex in the Youla parameter. This class includes SISO control problems with robust stability and robust disturbance attenuation as the design specifications. Function space duality theoy is used to establish an all-pass property.