H∞ controller reduction in trajectory sensitivity minimization

H_∞ optimal control design based on the trajectory sensitivity model is considered. The obtained controller, including the trajectory sensitivity model, is then transformed to a controller which has simple structure. Thereby, controller reduction can be addressed. Since the simplified controller may be unstable itself, a reduction scheme for an unstable transfer function is required. The article considers a left coprime factorization of a part of the generalized plant model and a right coprime factorization (r.c.f.) of the simplified controller so that a Bezout equation holds instead of a doubly coprime factorization. Then, the order of a transfer function which consists of the r.c.f. is reduced. Furthermore, a condition for internal stability in controller reduction is given. The effectiveness of the proposed method is verified by a numerical example