多胞型二维多项式的Schur稳定性

Schur Stability of Polytopes of Two-Dimensional Polynomials

本文提出多胞型二维多项式的Schur稳定的充分必要条件。我们揭示多胞型二维多项式的系数具有线性仿射特性。基于这一仿射特性，将多胞型二维多项式视为具有复变系数的多胞型一维多项式，我们证明多胞型二维多项式的稳定性可由其有限的棱边多项式的稳定性保证。我们提供了一种棱边多项式的稳定性检验算法。

The necessary and sufficient conditions of Schur stability of polytopes of two-dimensional (2-D) polynomials have been established. We reveal that the uncertain coefficients of the 2-D polytopes are of linear affine property. Based on the affine property, regarding polytopes of 2-D polynomials as the polytopes of 1-D polynomials with complex variable coefficients, we show that the stability of a polytope of 2-D polynomials can be guaranteed by that of finite edge polynomials of the polytope. An algorithm about the stability test of edge polynomials is provided.