Optimal Diagonal Scaling for Infinity Norm Optimization

A solution is presented for the previously unsolved diagonally scaled multivariable infinity-norm optimization problem of minimizing |D(s)(A(s) + ¿(s)X(s))D^-1(s)|¿ over the set of stable minimum-phase diagonal D(s) and stable X(s). This problem is of central importance in the synthesis of feedback control laws for robust stability and insensitivity in the presence of "structured" plant uncertainty. The result facilitates the design of feedback controllers which optimize the "excess stability margin [3]" (or, equivalently, the "structured singular value ¿ [4]") of diagonally perturbed feedback systems.