By Topic

On the irreducible Jordan form realization and the degree of a rational matrix

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)

A new method for realizing a rational transfer-function matrix, in the factored form, into an irreducible Jordan canonical form state equation is presented. The method consists of two steps. First, the irreducible Jordan form structure of the internal dynamics of the system is determined simply from the ranks of an augmented coefficient matrix and its submatrices, without actually having to construct a realization. Second, the augmented coefficient matrix is decomposed in a simple manner to obtain the final realization. The construction procedure is straightforward and allows one to choose explicitly the element values with a high degree of freedom. As a natural consequence of the irreducible realization, the rank of the augmented coefficient matrix associated with a pole is defined as the degree of the pole in question. This new definition is equivalent to the McMillan/Duffin-Hazony/Kalman degree. Using this definition, many well-known properties of the degree of a rational matrix are readily established.

Published in:

IEEE Transactions on Circuit Theory  (Volume:17 ,  Issue: 3 )