DocumentCode :
1190333
Title :
A general property of the transformation matrices associated with the n-variable bilinear transformation
Author :
Hertz, David ; Zeheb, Ezra
Volume :
31
Issue :
3
fYear :
1984
fDate :
3/1/1984 12:00:00 AM
Firstpage :
296
Lastpage :
299
Abstract :
By applying the bilinear transformation to a 
-variable polynomial, with 
, one arrives at a rational function, the zeros of which represent the "transformed polynomial." Let 
be the matrix relating the coefficients of the original polynomial to those of the transformed polynomial. It is shown that the matrix has a unique property, namely, 
, where 
is a positive constant which is explicitly derived for the various cases discussed, and 
is the unit matrix of the pertinent order.
-variable polynomial, with , one arrives at a rational function, the zeros of which represent the "transformed polynomial." Let be the matrix relating the coefficients of the original polynomial to those of the transformed polynomial. It is shown that the matrix has a unique property, namely, , where is a positive constant which is explicitly derived for the various cases discussed, and is the unit matrix of the pertinent order.Keywords :
Bilinear transformations; Matrices; Capacitance; Circuit synthesis; Design engineering; Differential equations; Digital filters; Linear matrix inequalities; Network synthesis; Polynomials; Stability; System testing;
fLanguage :
English
Journal_Title :
Circuits and Systems, IEEE Transactions on
Publisher :
ieee
ISSN :
0098-4094
Type :
jour
DOI :
10.1109/TCS.1984.1085489
Filename :
1085489
Link To Document :
