The simultaneous optimization problem for sensitivity and gain margin

The combined sensitivity and gain margin problem for single-input, single-output linear systems is formulated and solved using a complex function interpolation technique. It is proved that this problem always has a real rational solution provided it is solvable in the complex irrational sense. The sensitivity minimization problem subject to a gain margin constraint and its dual problem are also considered. In addition, the range of the gain margin constraint subject to which the optimal constrained sensitivity is identical to the optimal unconstrained sensitivity is given. It is shown that gain margin maximization conflicts with sensitivity minimization for a nonminimum phase plant