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Zero/pole structure of linear transfer functions
By: Wyman, B.F.; Perdon, A.M.; Conte, G.;
1985 / IEEE
This item was taken from the IEEE Periodical ' Zero/pole structure of linear transfer functions ' 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).