In this paper, we investigate the structure of the transfer function set which includes all eliminate the transfer functions deduced from the plant available information. It is shown that when an upper bound of the plant transfer function's H∞-norm has been supplied, and the noise contaminating the time domain identification experiment data is not too significant, such a transfer function set can be parameterized by a linear fractional transformation of two transfer function matrices. One of them is a fixed transfer function matrix which is completely determined by the plant available information and the noise magnitude. The other is a norm bounded, structure fixed, free transfer function matrix. Moreover, it is shown that the problem of analytically obtaining the fixed complexity nominal model that best approximates this transfer function set is as difficult as the μ-synthesis problem.