On effective criterion of stability of partial indices for matrix polynomials
On effective criterion of stability of partial indices for matrix polynomials
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DOI：
10.1098/rspa.2020.0012
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发表时间：
2020-06-24
影响因子：
3.5
通讯作者：
Adukov, V. M.
中科院分区：
文献类型：
--
作者：
Adukova, N. V.;Adukov, V. M.
本文给出了矩阵多项式部分指标在任意充分小扰动下稳定性的一个有效判据。验证的稳定性减少到两个明确定义的Toeplitz矩阵的秩的计算。此外，我们定义了一个概念的部分指标的稳定性在给定类的矩阵函数。这意味着我们将考虑一个允许的小扰动，使得扰动后的矩阵函数与原矩阵函数属于同一类。我们证明了在一类矩阵多项式的Gohberg-Krein-Bojarsky准则是保留的，即新的稳定情况下不会出现。我们在这个类中的稳定性准则的证明不使用Gohberg-Krein-Bojarsky定理。
In the work, we obtain an effective criterion of the stability of the partial indices for matrix polynomials under an arbitrary sufficiently small perturbation. Verification of the stability is reduced to calculation of the ranks for two explicitly defined Toeplitz matrices. Furthermore, we define a notion of the stability of the partial indices in the given class of matrix functions. This means that we will consider an allowable small perturbation such that a perturbed matrix function belong to the same class as the original one. We prove that in the class of matrix polynomials the Gohberg-Krein-Bojarsky criterion is preserved, i.e. new stability cases do not arise. Our proof of the stability criterion in this class does not use the Gohberg-Krein-Bojarsky theorem.