Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2008.14.12.1270

Wavelet-based Analysis for Singularly Perturbed Linear Systems Via Decomposition Method  

Kim, Beom-Soo (경상대학교 기계항공공학부, 해양산업연구소)
Shim, Il-Joo (대림대학 자동화시스템과)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.14, no.12, 2008 , pp. 1270-1277 More about this Journal
Abstract
A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.
Keywords
Haar wavelet; linear system; singular perturbation; sylvester equation; system decomposition;
Citations & Related Records

Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 M. Ohkita and Y. Kobayashi, 'An application of rationalized Haar functions to solution of linear differential equations.' IEEE Trans. Circuits Systems I. Fund. Theory Appl. vol. 9, pp. 853-862, 1986
2 Z. Gajic and M.T. Lim, Optimal Control Of Singularly Perturbed Linear Systems And Applications, Marcel Dekker, New York, 2001
3 F. Ding and T.W. Chen, 'Gradient based iterative algorithms for solving a class of matrix equations,' IEEE Tran. Automa. Contr., vol. 50, pp. 1216-1221, 2005   DOI   ScienceOn
4 H. R. Karimi, P. J. Maralani, B. Moshiri, and B. Lohmann, 'Numerically efficient approximations to the optimal control of linear singularly perturbed systems based on Haar wavelets,' Int. J. of Computer Mathematics, vol. 82, pp. 495-507, 2005   DOI   ScienceOn
5 R. S. Stankovic and B. J. Falkowski, 'The Haar wavelet transform: its status and achievements,' Computers and Electrical Engineering, vol. 29, no. 1, pp. 25-44, 2003   DOI   ScienceOn
6 C. H. Hsiao, 'Solution of variational problems via Haar orthonormal wavelet direct method,' Int. J. Comput. Math, vol. 81, pp. 871-887, 2004   DOI   ScienceOn
7 K. W. Chang, 'Singular perturbations of a general boundary value problems,' SIAM J. Math. Anal., vol. 3, pp. 520-526, 1972   DOI
8 G. H. Golub, S. Nash, and C. Van Loan, 'A Hessenberg-Schur Method for the Problem AX + XB = C,' IEEE Trans. Automa. Contr., vol. 24, pp. 909-913, 1979   DOI
9 Y. Arkun and S. Ramakrishnan, 'Bounds on the optimum quadratic cost of structure-constrained controllers,' IEEE Tran. Automa. Contr., vol. 28, pp. 924- 927, 1983   DOI
10 C. H. Hsiao and W. J. Wang, 'State analysis and parameter estimation of bilinear systems via Haar wavelets,' IEEE Trans. Circuits Systems I. Fundam. Theory Appl. vol. 47, pp. 246-250, 2000   DOI   ScienceOn
11 C. F. Chen and C. H. Hsiao, 'Haar wavelet method for solving lumped and distributed-parameter systems,' IEE Proc. Control Theory Appl. vol. 144, pp. 87-94, 1997   DOI   ScienceOn
12 G. Freiling, 'A survey of nonsymmetric Riccati equations,' Linear Algebra Appl., pp. 243-270, 2002
13 B. S. Kim, I. J. Shim, B. K. Choi, and J. H. Jeong, 'Wavelet based control for linear systems via reduced order Sylvester equation,' The 3rd Int. Conf. on Cooling and Heating Technologies, pp. 239-244, 2007
14 B. S. Kim and I. J. Shim 'Haar wavelet-based control for HVAC systems,' 2007 Int. Sym. On Advanced Intelligent Systems, pp. 647-650, 2007
15 A. Haar, 'Zur Theorie der orthogonaler Funktionensysteme,' Math. Ann. vol. 69, pp. 331-371, 1910   DOI
16 J. Brewer, 'Kronecker products and matrix calculus in system theory,' IEEE Trans. on Circuits and Systems, vol. 25, pp. 772-781, 1978   DOI