In this paper, a control system design that is applicable to both minimum and non-minimum-phase plants is discussed. The output of this system can follow an arbitrary reference output with a bounded input. In the first part of this paper we propose a new concept which is a bounded input calculation method of following a reference output. It is then used to design a model-following control system (MFCS) for multivariable non-minimum-phase plants. Corresponding to the right and left coprime factorizations of the plant, two MFCS designs are given. An extension of the MFCS to adaptive control is discussed and numerical examples are given to illustrate the effectiveness of the proposed adaptive system design.