Controller synthesis for plants subject to linear time invariant full structured uncertainty

Addresses the problem of synthesizing controllers for plants subject to a class of linear time invariant (LTI) uncertainty termed full structured uncertainty. Unlike the linear time varying case, the optimal controller for plants subject to LTI uncertainty is generally infinite dimensional. The solution is approximated by solving a succession of subproblems where the plant uncertainty is not LTI, but rather is allowed to shift the energy of signals in the frequency domain by a constrained amount; the exact solution to each of these subproblems is in the form of an affine matrix inequality. In the limiting case, as the amount of energy shifting is constrained to be zero, the derived conditions become necessary for arbitrarily slowly varying uncertainty, and for LTI uncertainty when the number of uncertainty blocks is less than or equal to four.