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"... This paper deals with a module theoretic approach to the dipolynomial matrix parametrization of discrete-time behaviour systems as introducted by Willems [1991]. Canonical minimal lag representations for these behaviours are constructed which are tighter than the corresponding polynomial representat ..."

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This paper deals with a module theoretic approach to the dipolynomial matrix parametrization of discrete-time behaviour systems as introducted by Willems [1991]. Canonical minimal lag representations for these behaviours are constructed which are tighter than the corresponding polynomial representations. 1 Introduction Matrices of rational functions play an important role in the description of the input/output behaviour of linear systems via transfer functions (matrices). With the introduction of minimal bases of rational vector spaces Forney [1975] gave elegant algebraic solutions for problems in the context of the input/output behaviour of linear systems; for example, problems of realization and invertibility of linear systems. For the algebraic description of the state space approach and the system description via polynomial matrices (introduced by Rosenbrock [1970]) modules over the polynomial ring are the relevant structures. The foundation for the module theoretic treatment of l...