区间矩阵多项式的Hurwitz与Schur鲁棒稳定性

Robust Hurwitz and Schur Stability of Interval Matrix Polynomials

由于N阶区间矩阵多项式的参数空间的维数最大可达 2NK2 维 ,采用有限检验算法确定其Hurwitz与Schur稳定性是很困难的 .为解决这一问题 ,本文提出的检验定理将李雅普诺夫函数与区间矩阵多项式的上下界联系起来 ,使区间矩阵多项式的Hurwitz与Schur稳定检验过程得以简化 ,为区间向量微分方程系统与区间离散时滞系统的鲁棒稳定性判定提供了一种方法 .

Since the parameter space of interval matrix polynomials with N order and K×K dimension is of 2NK 2\ dimension at most, it is difficult to determine their Hurwitz and Schur stability by finite test algorithms. To solve the problem, we propose two test theorems that relate Lyapunov function to the upper bound and the lower bound coefficient matrices of interval matrix polynomials, simplifying the stability test procedure of the problems. The theorems provide an approach to determine the robust stability of interval vector differential equation systems and discrete time_delay systems.