Reduced-order doubly coprime factorization in RH∞ and its applications

In the factorization approach, a doubly coprime factorization (DCF) is an elementary and powerful tool. For the calculation of DCF, the method proposed by Nett et al. is well known (1984). Their method is carried out by finding feedback and full-order observer gain for a given system. DCF using the reduced-order observer is also reported (Hippe, 1989, and Fujimore, 1993). In these papers, some elements in DCF are not proper transfer functions. So, a free parameter matrix is constrained to be strictly proper if we use the stabilizing controllers presented in Fujimore (1993). Therefore, these methods are not useful for the factorization approach. In this paper, we derive a reduced-order DCF using a polynomial approach. Then state space formulae are also given. Each element of the proposed DCF belongs to the set of RH_∞ , so it is useful for the factorization approach. The proposed method can be carried out by calculating feedback and reduced-order observer gain for a given system