- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Abstract and Applied Analysis

Volume 2014 (2014), Article ID 285086, 9 pages

http://dx.doi.org/10.1155/2014/285086

## A Real Representation Method for Solving Yakubovich--Conjugate Quaternion Matrix Equation

^{1}School of Mathematics, Shandong University, Jinan 250100, China^{2}College of Information Science and Engineering, Shandong University of Science and Technology,
Qingdao 266590, China^{3}School of Astronautics, Harbin Institute of Technology, Harbin 150001, China^{4}College of Mathematics Science, Liaocheng University, Liaocheng 252059, China

Received 19 October 2013; Revised 12 December 2013; Accepted 14 December 2013; Published 12 January 2014

Academic Editor: Ngai-Ching Wong

Copyright © 2014 Caiqin Song 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.

#### Linked References

- R. R. Bitmead, “Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations,”
*IEEE Transactions on Automatic Control*, vol. 26, no. 6, pp. 1291–1294, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - B. H. Kwon and M. J. Youn, “Eigenvalue-generalized eigenvector assignment by output feedback,”
*IEEE Transactions on Automatic Control*, vol. 32, no. 5, pp. 417–421, 1987. View at Google Scholar - D. G. Luenberger, “An introduction to observers,”
*IEEE Transactions on Automatic Control*, vol. 16, pp. 596–602, 1971. View at Google Scholar - C.-C. Tsui, “New approach to robust observer design,”
*International Journal of Control*, vol. 47, no. 3, pp. 745–751, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Chen, R. J. Patton, and H.-Y. Zhang, “Design of unknown input observers and robust fault detection filters,”
*International Journal of Control*, vol. 63, no. 1, pp. 85–105, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. Park and G. Rizzoni, “An eigenstructure assignment algorithm for the design of fault detection filters,”
*IEEE Transactions on Automatic Control*, vol. 39, no. 7, pp. 1521–1524, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. Yuan and A. Liao, “Least squares solution of the quaternion matrix equation $X-A\widehat{X}B=C$ with the least norm,”
*Linear and Multilinear Algebra*, vol. 59, no. 9, pp. 985–998, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - S. F. Yuan, A. P. Liao, and G. Z. Yao, “The matrix nearness problem associated with the quaternion matrix equation $AX\text{\hspace{0.17em}}{A}^{H}+BY\text{\hspace{0.17em}}{B}^{H}=C$,”
*Journal of Applied Mathematics and Computing*, vol. 37, no. 1-2, pp. 133–144, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - C. Song and G. Chen, “On solutions of matrix equation $XF-AX=C$ and $XF-A\tilde{X}=C$ over quaternion field,”
*Journal of Applied Mathematics and Computing*, vol. 37, no. 1-2, pp. 57–68, 2011. View at Publisher · View at Google Scholar · View at MathSciNet - C. Q. Song, G. L. Chen, and X. D. Wang, “On solutions of quaternion matrix equations $XF-AX=BY$ and $XF-A\tilde{X}=BY$,”
*Acta Mathematica Scientia*, vol. 32, no. 5, pp. 1967–1982, 2012. View at Google Scholar - S. Ling, M. Wang, and M. Wei, “Hermitian tridiagonal solution with the least norm to quaternionic least squares problem,”
*Computer Physics Communications*, vol. 181, no. 3, pp. 481–488, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. H. Wang, M. S. Wei, and Y. Feng, “An iterative algorithm for least squares problem in quaternionic quantum theory,”
*Computer Physics Communications*, vol. 179, no. 4, pp. 203–207, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. S. Jiang and M. S. Wei, “On a solution of the quaternion matrix equation $X-A\tilde{X}B=C$ and its application,”
*Acta Mathematica Sinica*, vol. 21, no. 3, pp. 483–490, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - T. Jiang and M. Wei, “On solutions of the matrix equations $X-AXB=C$ and $X-A\overline{X}B=C$,”
*Linear Algebra and Its Applications*, vol. 367, pp. 225–233, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - L. Huang, “The quaternion matrix equation $\sum {A}^{i}X{B}_{i}$,”
*Acta Mathematica Sinica*, vol. 14, no. 1, pp. 91–98, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. H. Bevis, F. J. Hall, and R. E. Hartwig, “Consimilarity and the matrix equation $A\overline{X}-XB=C$,” in
*Current Trends in Matrix Theory*, pp. 51–64, North-Holland, New York, NY, USA, 1987. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - J. H. Bevis, F. J. Hall, and R. E. Hartwig, “The matrix equation $A\overline{X}-XB=C$ and its special cases,”
*SIAM Journal on Matrix Analysis and Applications*, vol. 9, no. 3, pp. 348–359, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - B. Hanzon, “A faddeev sequence method for solving Lyapunov and Sylvester equations,”
*Linear Algebra and Its Applications*, vol. 241, pp. 401–430, 1996. View at Google Scholar - A.-G. Wu, G.-R. Duan, and H.-H. Yu, “On solutions of the matrix equations $XF-AX=C$ and $XF-A\overline{X}=C$,”
*Applied Mathematics and Computation*, vol. 183, no. 2, pp. 932–941, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - A.-G. Wu, Y.-M. Fu, and G.-R. Duan, “On solutions of matrix equations $V-AVF=BW$ and $V-A\overline{V}F=BW$,”
*Mathematical and Computer Modelling*, vol. 47, no. 11-12, pp. 1181–1197, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - B. Hanzon and R. M. Peeters, “A Feddeev sequence method for solving Lyapunov and Sylvester equations,”
*Linear Algebra and Its Applications*, vol. 241–243, pp. 401–430, 1996. View at Google Scholar - A.-G. Wu, H.-Q. Wang, and G.-R. Duan, “On matrix equations $X-AXF=C$ and $X-A\overline{X}F=C$,”
*Journal of Computational and Applied Mathematics*, vol. 230, no. 2, pp. 690–698, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet