A frequency-specific enhanced approach to transfer function approximation

This paper investigates the problem of frequency-specific (FS) model approximation of transfer functions. The objective is to find an approximation transfer function for a higher-order one such that the approximation error over a specific frequency range is minimized. The importance of this problem lies that, in practice, a better approximation performance within a certain frequency range is often required than that outside the frequency range. First, a linear matrix inequality condition characterizing the FS gain performance of a transfer function is derived by the generalized Kalman-Yakubovich-Popov lemma, and then a simple iterative approach based on an upper-bounding technique is proposed to optimize the approximation model. Numerical experiment shows that the proposed approach is more effective in enhancing the approximation performance over a specific frequency range than some existing approaches.