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Abstract and Applied Analysis
Volume 2014, Article ID 301375, 7 pages
Research Article

Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

1Unit 302, Department of Automation, Xi’an Institute of High-Tech, Xi’an, Shaanxi 710025, China
2Beijing City, Haidian District, Qinghe Building D7, Beijing 100085, China

Received 18 July 2014; Accepted 5 August 2014; Published 18 August 2014

Academic Editor: Zheng-Guang Wu

Copyright © 2014 Hua-Feng He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.