A geometric approach to the inversion of multivariable systems

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Abstract
The input and output matrix maps B and C of a linear multivariable system S(A,B,C) play an important role in determining the behaviour of the system. Square systems with the produce CB full rank possess a simple state-space geometry which is deployed in the present paper for the derivation of an explicit state-space characterization of the inverse system. An efficient algorithm for the inversion of a system is then obtained. The elegance of the results discussed enables the examination of the duality between poles/modes and zeros/zero-directions. Finally, an extension of the above to systems with CB rank-deficient is undertaken