Generalized systems: pencils, modules, and pole spaces

A bridge between generalized system representations and module theory is provided. By means of a theorem, the little pole space associated with a generalized system is shown to be isomorphic to the global system pole space, a module-theoretic concept incorporating both finite and infinite system pole information. These results hold true for any regular matrix pencil (zE-A), and may be interpreted as special cases in terms of causal and anticausal systems. An illustration of the theorem using the Weierstrass form is given.<>