System order and structure indices of linear systems in polynomial form

Abstract

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