Zero/pole structure of linear transfer functions

Zero/pole structure of linear transfer functions,10.1109/CDC.1985.268498,G. Conte,A. M. Perdon,B. F. Wyman

Zero/pole structure of linear transfer functions   (Citations: 1)
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This paper studies the relationship between the zeros and poles of a linear transfer function from a module-theoretic point of view. The situation is well-understood when G(z) is proper, so that the pole module at infinity vanishes and (as always) the polynomial pole module X serves as the state space of the minimal realization (X;A,B,C) of G(z). There are isomorphisms identifying the (polynomial) zero module Z(G) with V*, the maximum (A,B)-invariant subspace of X contained in ker C, and the infinite zero module Z¿ (G) with S*, the minimum conditionally invariant subspace of X containing im B [1,2,7]. Our results here show that these two facts can be unified by using exact sequences which require no properness assumptions on G(z).
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    • ...We will not develop here a complete treatement of the case of poles and zeros at infinity (see [4,6,7,9,10,26] for applications), but we will simply point out its general lines, assuming that the reader is familiar with the classical notions...

    G. Conteet al. Zeros, poles and modules in linear system theory

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