论文信息 - Schur stability of polytopes of bivariate polynomials

Schur stability of polytopes of bivariate polynomials

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.

Rolf Unbehauen | Xiyu Du | Yang Xiao

[1] R. Unbehauen,et al. New stability test algorithm for two-dimensional digital filters , 1998 .

[2] Boris Polyak,et al. Frequency domain criteria for robust stability of bivariate polynomials , 1994 .

[3] Thomas S. Huang,et al. Stability of two-dimensional recursive filters , 1972 .

[4] E. A. Hadjiconstantinou. Algorithms for two-dimensional cutting problems , 1988 .

[5] B. T. Polyak,et al. Frequency domain criteria for l/sup p/-robust stability of continuous linear systems , 1991 .

[6] V.L. Kharitonov,et al. Stability and robust stability of multivariate polynomials , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[7] Huang Lin,et al. Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[8] N. K. Bose,et al. Invariance of the strict Hurwitz property for bivariate polynomials under coefficient perturbations , 1988 .