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Extension of gauthier's method for multivariable realizations by incorporating coprime fractions

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This paper presents an extension of Gauthier's algorithm, which solves the problem of searching for the multivariable minimal realization starting from square transference matrices. Previously, the algorithm incorporates the coprime fractions developed with Silvester matrices and qr factorization. Since the coprime fractions have a special relation with matrices in polynomial fraction, they show their differences by analyzing them independently. The general features are set out, and the developed functions named, in order to emphasize the different search paths and their representation in state space (neither of which are not unique) for the co-prime fraction. For demonstration we used a multivariable dynamic system, where the efficiency and limitations of the developed algorithm are checked based on the functions performed with the Matlab® Control Toolbox.

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