DocumentCode :
844085
Title :
Proper and stable, minimal MacMillan degrees bases of rational vector spaces
Author :
Vardulakis, Antonis I.G. ; Karcanias, Nicos
Author_Institution :
Aristotle University of Thessaloniki, Greece
Volume :
29
Issue :
12
fYear :
1984
fDate :
12/1/1984 12:00:00 AM
Firstpage :
1118
Lastpage :
1120
Abstract :
The structure of proper and stable bases of rational vector spaces is investigated. We prove that if 
is a rational vector space, then among the proper bases of 3(s) there is a subfamily of proper bases which are 1) stable, 2) have no zeros in 
and therefore are column (row) reduced at infinity, and 3) their MacMillan degree is minimum among the MacMillan degrees of all other proper bases of 3(s) and it is given by the sum of the MacMillan degrees of their columns taken separately. It is shown that this notion is the counterpart of Forney\´s concept of a minimal polynomial basis for the family of proper and stable bases of 3(s).
is a rational vector space, then among the proper bases of 3(s) there is a subfamily of proper bases which are 1) stable, 2) have no zeros in and therefore are column (row) reduced at infinity, and 3) their MacMillan degree is minimum among the MacMillan degrees of all other proper bases of 3(s) and it is given by the sum of the MacMillan degrees of their columns taken separately. It is shown that this notion is the counterpart of Forney\´s concept of a minimal polynomial basis for the family of proper and stable bases of 3(s).Keywords :
Rational functions; Vector spaces; H infinity control; Mathematics; Poles and zeros; Polynomials; Tin;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1984.1103456
Filename :
1103456
Link To Document :
