Control relevant identification for H∞-norm based performance specifications

For consecutive model-based control design, approximate identification of linear models should be performed on the basis of a feedback-relevant criterion, compatible with the control design. For an H_∞-norm based control design, a procedure is presented to estimate a possibly unstable and feedback controlled plant by using an H_∞-norm based feedback-relevant identification criterion. It is shown that the formulated identification problem can be handled by taking (noisy) closed loop frequency domain measurements of the plant and fitting a model of a prespecified McMillan degree, which is parametrized in a stable factorization, using a certain nonlinear constrained minimization. The procedure is illustrated by an example