Schur stability of polytopes of bivariate polynomials
Yang Xiao, Rolf Unbehauen, Xiyu Du · 1999
The necessary and sufficient conditions of Schur stability of polytopes of bivariate polynomials have been established. Based on a simplification, the 2D analysis for stability of polytopes of 2D polynomials is turned into that of polytopes of 1D polynomials with complex variable coefficients. We reveal that the uncertain coefficients of the 2D polytopes are of linear affine property; then we 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.