This note presents some new results in linear systems. First, the relationship between the polynomial matrix description and the state-space representation of multivariable systems is clarified. Then, we show that once such a relationship is determined, the coprime matrix fraction description can be easily computed. And we can further develop a closed-form formula to solve the pole-assignment problem of multivariable systems. Such formula can be thought of as an extension of the Ackermann's formula for multi-input/multi-output (MIMO) systems. Thus this note potentially gives us a clearer insight into linear systems from the theoretical viewpoint.
