A NEW APPROACH FOR COMPUTING THE STATE-FEEDBACK GAINS OF MULTIVARIABLE SYSTEMS

This note presents some new results in linear systems. First, the rela tionship between the polynomial matrix description and the state-space representation of multivariable systems is clarified. Then, we show t hat once such a relationship is determined, the coprime matrix fractio n description can be easily computed. And we can further develop a clo sed-form formula to solve the pole-assignment problem of multivariable systems. Such formula can be thought of as an extension of the Ackerm ann's formula for multi-input/multi-output (MIMO) systems. Thus this n ote potentially gives us a clearer insight into linear systems from th e theoretical viewpoint.