The discrete multidimensional MPUM

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Given a finite set of polynomial-exponential, multivariate, and vector-valued sequences, we show how the smallest linear shift-invariant set containing the data trajectories can be written as the solution set of a system of linear difference equations with constant coefficients. The resulting representation is known as the most powerful unfalsified model (MPUM) in behavioral systems theory. We address the case where the components of the given sequences take their values in a field, as well as the case where these values belong to a finite ring of the form ℤ/mℤ for an integer m > 1.

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