About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 285086, 9 pages
http://dx.doi.org/10.1155/2014/285086
Research Article

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

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

  1. 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
  2. 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.
  3. D. G. Luenberger, “An introduction to observers,” IEEE Transactions on Automatic Control, vol. 16, pp. 596–602, 1971.
  4. 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
  5. 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
  6. 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
  7. S. Yuan and A. Liao, “Least squares solution of the quaternion matrix equation XAX^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
  8. S. F. Yuan, A. P. Liao, and G. Z. Yao, “The matrix nearness problem associated with the quaternion matrix equation AXAH+BYBH=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
  9. C. Song and G. Chen, “On solutions of matrix equation XFAX=C and XFAX˜=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
  10. C. Q. Song, G. L. Chen, and X. D. Wang, “On solutions of quaternion matrix equations XFAX=BY and XFAX˜=BY,” Acta Mathematica Scientia, vol. 32, no. 5, pp. 1967–1982, 2012.
  11. 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
  12. 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
  13. T. S. Jiang and M. S. Wei, “On a solution of the quaternion matrix equation XAX˜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
  14. T. Jiang and M. Wei, “On solutions of the matrix equations XAXB=C and XAX¯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
  15. L. Huang, “The quaternion matrix equation AiXBi,” 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
  16. J. H. Bevis, F. J. Hall, and R. E. Hartwig, “Consimilarity and the matrix equation AX¯XB=C,” in Current Trends in Matrix Theory, pp. 51–64, North-Holland, New York, NY, USA, 1987. View at Zentralblatt MATH · View at MathSciNet
  17. J. H. Bevis, F. J. Hall, and R. E. Hartwig, “The matrix equation AX¯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
  18. B. Hanzon, “A faddeev sequence method for solving Lyapunov and Sylvester equations,” Linear Algebra and Its Applications, vol. 241, pp. 401–430, 1996.
  19. A.-G. Wu, G.-R. Duan, and H.-H. Yu, “On solutions of the matrix equations XFAX=C and XFAX¯=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
  20. A.-G. Wu, Y.-M. Fu, and G.-R. Duan, “On solutions of matrix equations VAVF=BW and VAV¯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
  21. 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.
  22. A.-G. Wu, H.-Q. Wang, and G.-R. Duan, “On matrix equations XAXF=C and XAX¯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