Model reduction of linear systems over finite-frequency intervals via frequency-dependent balanced truncation: Singleton case

The finite-frequency model reduction problem (FFMRP) was revisited, reformulated and rediscovered in this paper. Inspired by the Generalized KYP (GKYP) Lemma and classic balanced truncation (BT) method, it is conceived and believed that there exists a generalized frequency dependent balanced truncation (FDBT) method solving the FFMRP perfectly. For the special singleton case (i.e. the system´s operating at a fixed frequency), the conceived FDBT was successful developed. FDBT generate reduced-order model with an explicit frequency dependent approximation error bound which is not greater than the error bound obtained by the classic BT. A ladder RLC circuit example was carried out to illustrate the advantage of FDBT. Although the FDBT in this paper was incomplete and cannot deal with the general finite-frequency cases, it is believed that this results paved the way for the final solution of FFMRP.