A new computationally simple algorithm is presented for calculating coprime matrix fraction description, and minimal state space representation of a multivariable linear system, specified by a transfer function matrix. The algorithm is based on a theorem derived in the paper which permits the calculation of the order of the minimal realization, as well as the observability indices (column degrees) directly from the coefficients of the given transfer function matrix. Existing minimal realization and coprime factorization algorithms are reviewed and compared with the proposed procedure. An illustrative example is given to show feasibility of the suggested method.
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