ABSTRACT

For a family of real matrices with entries polynomially depending on parameters, symbolic algorithms are proposed for verification of the Routh – Hurwitz stability under parameter variations in a given box, and for the distance to instability computation in the case of perturbations over $\mathbb{C}$. Both problems are reduced to the analysis of real zeros of a pair of univariate polynomials; one of these reductions is based on the discriminant computation in the Hankel determinant form. We also discuss a potential application of the suggested approach for finding an estimation for the accuracy of the distance to instability computations via numerical procedures.

中文翻译：

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多项式矩阵族的稳定性和不稳定性距离。复杂的扰动

摘要

对于具有多项式依赖于参数的条目的实矩阵族，提出了符号算法来验证给定框中参数变化下的 Routh-Hurwitz 稳定性，以及在扰动的情况下计算到不稳定性的距离$\mathbb{C}$. 这两个问题都归结为分析一对单变量多项式的实零点；这些减少之一是基于汉克尔行列式形式的判别计算。我们还讨论了建议的方法的潜在应用，用于通过数值程序找到对不稳定性计算距离的准确性的估计。