<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an <italic>irreducible-at-infinity</italic> generalized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts of <italic>irreducibility</italic> and <italic>minimality</italic> of generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts of <italic>dynamic</italic> and <italic>non-dynamic</italic> variables appearing in generalized state space realizations are also examined.</p></abstract>

We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an irreducible-at-infinity generalized state space realization of a polynomial matrix is defined and the mechanism of the "cancellations" of "decoupling zeros at infinity" is closely examined. The difference between the concepts of irreducibility and minimality of generalized state space realizations of polynomial (transfer function) matrices is pointed out and the associated concepts of dynamic and non-dynamic variables appearing in generalized state space realizations are also examined.

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54 006, Greece

Department of Sciences, Technical Educational Institute of Thessaloniki, Sindos 574 00, Greece

General Department of Applied Science, Technical University of Chalkis, Psahna 34 400, Eubea, Greece

International Journal of Applied Mathematics and Computer Science

We review the realization theory of polynomial (transfer function) matrices via "pure" generalized state space system models. The concept of an...

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

Published Online: Apr 02, 2009

Page range: 77 - 88

DOI: https://doi.org/10.2478/v10006-009-0007-5

Keywords
polynomial matrices, realization theory, minimality, irreducibility, generalized state space, infinite decoupling zeros

This content is open access.

On the Realization Theory of Polynomial Matrices and the Algebraic Structure of Pure Generalized State Space Systems

Published Online: Apr 02, 2009

Page range: 77 - 88

DOI: https://doi.org/10.2478/v10006-009-0007-5

Keywordspolynomial matrices, realization theory, minimality, irreducibility, generalized state space, infinite decoupling zeros

This content is open access.

Keywords
polynomial matrices, realization theory, minimality, irreducibility, generalized state space, infinite decoupling zeros