An iterative method for computing robustness of polynomial stability

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• 作者：Nicola Guglielmi^a ; ^b ; ^{guglielm@univaq.it" class="auth_mail" title="E-mail the corresponding author} ; Manuela Manetta^c ; ^{manetta@math.gatech.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15A18 ; 65K05
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：292
• 期：Complete
• 页码：638-653
• 全文大小：620 K

文摘

We propose a method for computing the distance of a stable polynomial to the set of unstable ones (both in the Hurwitz and in the Schur case). The method is based on the reformulation of the problem as the structured distance to instability of a companion matrix associated to a polynomial. We first introduce the structured 05318113f68e2c3cbcb932b523263d4" title="Click to view the MathML source">蔚$蔚$-pseudospectrum of a companion matrix and write a system of ordinary differential equations which maximize the real part (or the absolute value) of elements of the structured 05318113f68e2c3cbcb932b523263d4" title="Click to view the MathML source">蔚$蔚$-pseudospectrum and then exploit the knowledge of the derivative of the maximizers with respect to 05318113f68e2c3cbcb932b523263d4" title="Click to view the MathML source">蔚$蔚$ to devise a quadratically convergent iteration. Furthermore we use a variant of the same ODEs to compute the boundary of structured pseudospectra and compare them to unstructured ones. An extension to constrained perturbations is also considered.