Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 323080, 16 pages
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.


An efficient computational method is presented for state space analysis of singular systems via Haar wavelets. Singular systems are those in which dynamics are governed by a combination of algebraic and differential equations. The corresponding differential-algebraic matrix equation is converted to a generalized Sylvester matrix equation by using Haar wavelet basis. First, an explicit expression for the inverse of the Haar matrix is presented. Then, using it, we propose a combined preorder and postorder traversal algorithm to solve the generalized Sylvester matrix equation. Finally, the efficiency of the proposed method is discussed by a numerical example.