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Transfer-function-matrix realization in multivariable systems

This paper considers the realisation of a multivariable system Transfer Function Matrix (TFM) using a new systematic approach to the closed-loop pole-zero assignment. It is shown that complete control of the individual TFM elements can be achieved by obtaining complete control over the state-space matrices {A,B,C ,D} in a systematic way. In terms of the TFM, this is achieved by producing any desired poles and any desired single row and column of numerator polynomials. The method utilises all of the available degrees of freedom and is sufficient to produce an arbitrary nth-order TFM. New transformation matrices M and V play an important role in the relationship between the state-variable matrix forms and the poles and zeros of the individual elements of the TFM, as well as in computation of required feedback and feedforward gains,