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

TL;DR

This paper introduces a new multi-step approach for partial pole assignment in symmetric quadratic pencils with time delay, efficiently repositioning undesired eigenvalues while keeping others unchanged.

Contribution

The paper presents a novel multi-step method that transforms the problem into solving low-order linear systems, improving efficiency for large systems with few poles to reassign.

Findings

Effective pole reassignment demonstrated through numerical examples.

Method reduces problem to solving $p^2$ linear systems.

High efficiency for large systems with few poles to reassign.

Abstract

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