A new approach for computing the state feedback gains of multivariable systems

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 MIMO systems. Thus this note potentially gives us a clearer insight into linear systems from the theoretical viewpoint