Abstract

Linear time-invariant, finite dimensional discrete time systems very often are specified in a polynomial form representation in either a forward or backward shift operator (sometimes called MFD and ARMA form). Considering dynamical systems in terms of their behaviour, i.e. the set of admissible signal trajectories, it is shown that there exists a unifying theory for the determination of McMillan degree and Kronecker indices of systems represented by polynomial matrices in the two shift operators, considering the MFD and ARMA forms as special cases. Moreover the notions of McMillan degree and Kronecker indices can be generalized to noncontrollable and noncausal systems.

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