A novel multi-step method for the partial pole assignment in symmetric quadratic pencil with time delay

07/02/2023

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by   Qing Liu, et al.

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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