In this paper, we study the partial pole assignment problem in symmetric quadratic pencil with time delay. A novel multi-step method is proposed to solve this problem, resulting in the undesired eigenvalues being moved to desired values, and the remaining eigenvalues unchanged. By establishing a new matrix equality relation and using a multi-step method, the problem is transformed into solving linear systems with low order. Specifically, assuming that there are $p$ undesired eigenvalues requiring reassigned, the size of the linear system we finally solved is $p^2$. Notably, the method demonstrates high efficiency for large systems with only a few poles requiring reassigned. Numerical examples are provided to illustrate the effectiveness of the proposed method

翻译：本文研究了时滞对称二次束中的部分极点配置问题。提出了一种新型多步方法来求解该问题，可将非期望特征值移至期望值，同时保持其余特征值不变。通过建立新的矩阵等式关系并采用多步方法，该问题被转化为低阶线性系统的求解。具体而言，假设有 $p$ 个需要重新配置的非期望特征值，最终求解的线性系统规模为 $p^2$。值得注意的是，该方法对于仅需重新配置少量极点的大规模系统具有极高的效率。数值算例验证了所提方法的有效性。