Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 323080, 16 pages
doi:10.1155/2008/323080
Research Article

Combined Preorder and Postorder Traversal Algorithm for the Analysis of Singular Systems by Haar Wavelets

Beom-Soo Kim,1 Il-Joo Shim,2 Myo-Taeg Lim,3 and Young-Joong Kim3

1School of Mechanical and Aerospace Engineering, Gyeongsang National University, 445 Inpyeong-Dong, Tongyeong, Gyeongnam 650-160, South Korea
2Department of Automatic System Engineering, Daelim College, 526-7 Bisan-Dong, Anyang, Gyeonggi 431-715, South Korea
3School of Electrical Engineering, Korea University, 1-5 Anam-dong, Sungbuk-gu, Seoul, 136-701, South Korea

Received 31 May 2008; Accepted 25 August 2008

Academic Editor: Carlo Cattani

Copyright © 2008 Beom-Soo Kim 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. C. Cattani, “Haar wavelet-based technique for sharp jumps classification,” Mathematical and Computer Modelling, vol. 39, no. 2-3, pp. 255–278, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. C. Cattani, “Wavelet approach to stability-of-orbits analysis,” International Applied Mechanics, vol. 42, no. 6, pp. 721–727, 2006. View at Publisher · View at Google Scholar
  3. C. F. Chen and C. H. Hsiao, “Haar wavelet method for solving lumped and distributed-parameter systems,” IEE Proceedings: Control Theory and Applications, vol. 144, no. 1, pp. 87–94, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. C. F. Chen and C.-H. Hsiao, “Wavelet approach to optimising dynamic systems,” IEE Proceedings: Control Theory and Applications, vol. 146, no. 2, pp. 213–219, 1999. View at Publisher · View at Google Scholar
  5. F. L. Lewis, “A survey of linear singular systems,” Circuits, Systems, and Signal Processing, vol. 5, no. 1, pp. 3–36, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. L. Lewis and B. G. Mertzios, “Analysis of singular systems using orthogonal functions,” IEEE Transactions on Automatic Control, vol. 32, no. 6, pp. 527–530, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Kalpana and S. R. Balachandar, “Haar wavelet method for the analysis of transistor circuits,” AEU - International Journal of Electronics and Communications, vol. 61, no. 9, pp. 589–594, 2007. View at Publisher · View at Google Scholar
  8. C. F. van Loan, “The ubiquitous Kronecker product,” Journal of Computational and Applied Mathematics, vol. 123, no. 1-2, pp. 85–100, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. A. Haar, “Zur Theorie der orthogonalen Funktionensysteme,” Mathematische Annalen, vol. 69, no. 3, pp. 331–371, 1910. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Z. Gajic and M. T. J. Qureshi, Lyapunov Matrix Equation in System Stability and Control, vol. 195 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1995. View at MathSciNet
  11. B.-S. Kim, I.-J. Shim, B. K. Choi, and J. H. Jeong, “Wavelet based control for linear systems via reduced order Sylvester equation,” in Proceedings of the 3rd International Conference on Cooling and Heating Technologies (ICCHT '07), pp. 239–244, Tokyo, Japan, July 2007. View at MathSciNet
  12. F. Carrano and W. Savitch, Data Structures and Abstractions with Java, Prentice Hall, Upper Saddle River, NJ, USA, 2003. View at MathSciNet