Title :
Schur stability of polytopes of bivariate polynomials
Author :
Xiao, Yang ; Unbehauen, Rolf
Author_Institution :
Inst. of Inf. Sci., Northern Jiaotong Univ., Beijing, China
fDate :
7/1/2002 12:00:00 AM
Abstract :
Necessary and sufficient conditions for Schur stability of polytopes of bivariate polynomials have been established. Based on a simplification, the two-dimensional (2-D) analysis for stability of polytopes of 2-D polynomials is turned into that of polytopes of one-dimensional (1-D) polynomials with complex variable coefficients. We reveal that the uncertain coefficients of the 2-D polytopes possess a linear affine property, and then show that the stability of a polytope of bivariate polynomials can be guaranteed by that of finite edge polynomials of the polytope. An algorithm for the stability test of edge polynomials is provided
Keywords :
discrete systems; polynomials; stability; uncertain systems; 2-D polynomials; Schur stability; bivariate polynomials; complex variable coefficients; finite edge polynomials; guaranteed polytope stability; linear affine property; necessary sufficient conditions; one-dimensional polynomials; polytopes; robust stability; stability test algorithm; two-dimensional analysis; uncertain coefficients; uncertain two-dimensional discrete systems; Circuit stability; Frequency domain analysis; Information science; Polynomials; Robust stability; Stability analysis; Stability criteria; Sufficient conditions; System testing; Two dimensional displays;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
DOI :
10.1109/TCSI.2002.800839
