Title :
A continuity proof of Rudin´s theorem for polynomials and a generalization
Author :
Curtin, Eugene ; Saba, Salim
Author_Institution :
Dept. of Math., Southwest Texas State Univ., San Marcos, TX, USA
fDate :
9/1/2000 12:00:00 AM
Abstract :
We assign to each nonzero complex polynomial the minimum of the absolute values of its roots. We show the simple principle that this minimum depends continuously on the coefficients of the polynomial and is sufficiently powerful to give a very elementary proof of Rudin´s stability theorem for multivariable polynomials. Moreover, we show that the polynomial version of a generalization on Rudin´s theorem due to Hertz and Zeheb is obtained as a consequence of this principle.
Keywords :
multidimensional systems; polynomials; stability; Rudin´s theorem; continuity proof; multidimensional systems; multivariable polynomials; nonzero complex polynomial; stability theorem; Circuits; Digital filters; Digital signal processing; Mathematics; Multidimensional signal processing; Multidimensional systems; Polynomials; Stability criteria; Testing;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on