Your Search Results

Use this resource - and many more! - in your textbook!

AcademicPub holds over eight million pieces of educational content for you to mix-and-match your way.

Experience the freedom of customizing your course pack with AcademicPub!
Not an educator but still interested in using this content? No problem! Visit our provider's page to contact the publisher and get permission directly.

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).