Optimal H∞ synthesis of robust controllers for systems with structured uncertainty

A finite-dimensional nonlinear program is shown to yield the solution to the diagonally scaled multivariable L
^∞
optimization problem: min || D(s)(T
₁₁
(s) + T
₁₂
(S)Q(s)T
₂₁
(s))D-1(s) ||
_∞
D,D-1, Qε(H)
^n×n
. D diagonal for the case of square T
₁₂
,T
₂₁
,T
₁₁
εH
^∞
)
^n×n
. 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 solution to this problem facilitates the design of multivariable feedback controllers which optimize the "excess stability margin" [3] (or, equivalently, the structured singular value μ [4]) of diagonally perturbed feedback systems.