In this paper, we address the problem of computing the nearest linearly structured polynomial matrix with prescribed distinct eigenvalues. The problem deals with the computation of the minimal structured perturbation to the coefficient matrices so that the perturbed polynomial matrix has the prescribed eigenvalues and is the nearest to the given polynomial matrix. In recent years, a series of papers have been published on the perturbation of polynomial matrices with prescribed eigenvalues; however, a linear structure-preserving result does not exist so far to the best of our knowledge. In this paper, we have proposed an optimization based approach where we have reformulated the problem as a constrained optimization problem. Towards the end, a few numerical case studies are presented which demonstrate the efficiency and usefulness of our proposed method.

在本文中，我们解决了计算具有规定的不同特征值的最近线性结构多项式矩阵的问题。该问题涉及计算对系数矩阵的最小结构扰动，以便扰动的多项式矩阵具有规定的特征值并且最接近给定的多项式矩阵。近年来，已经发表了一系列关于具有规定特征值的多项式矩阵的摄动的论文；然而，据我们所知，目前还不存在保持线性结构的结果。在本文中，我们提出了一种基于优化的方法，我们将问题重新表述为约束优化问题。接近尾声，