On the robustness of multivariable linear feedback systems

One of the useful indicators of the robustness of a multivariable linear feedback system is the largest singular value of the nominal closed-loop transfer matrix. It is shown that while comparing different, not necessarily diagonal, closed-loop transfer matrices which have the same diagonal elements, the diagonal closed-loop transfer matrix has the greatest robustness. For plants with not "too" large parameter uncertainty, this result also guarantees the maximization of disturbance rejection, and the minimization of the control signal "power" at the plant's input.