Structured eigenvalue backward errors of Rosenbrock systems and related μ-value problems

2024/05/20 by Anshul Prajapati, Punit Sharma, Prajapati, Anshul +1
Computer Science · Engineering · Mathematics · #Advanced Research in Systems and Signal Processing #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.2405.11974

openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we compute the structured eigenvalue backward error of a Rosenbrock system matrix S(z)=[A-zI · amp; B
C · amp; P(z)] for a given scalar λ∈ \mathbb C. We have developed simplified formulas for the structured eigenvalue backward error of the Rosenbrock system matrix, considering both full and partial block perturbations. These formulas involve computing structured μ-values of a rectangular matrix under rectangular-block-diagonal perturbations. For the reformulated μ-value problem, we provide an explicit expression using partial isometric matrices and also obtain a computable upper bound, which is equal to the μ-value when the pertrubation matrix has no more than three blocks at the diagonal. The results are illustrated through numerical experiments.

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