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

Recommended by Carlo Cattani

Abstract

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.