The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지

Linear system analysis via wavelet-based pole assignment

웨이블릿 기반 극점 배치 기법에 의한 선형 시스템 해석

  • 김범수 (경상대학교 기계항공공학부, 해양산업연구소) ;
  • 심일주 (대림대학 자동화시스템과)
  • Published : 2008.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

Numerical methods for solving the state feedback control problem of linear time invariant system are presented in this paper. The methods are based on Haar wavelet approximation. The properties of Haar wavelet are first presented. The operational matrix of integration and its inverse matrix are then utilized to reduce the state feedback control problem to the solution of algebraic matrix equations. The proposed methods reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity and applicability of the proposed methods.

Keywords

References

  1. K. Maleknejad, R. Mollapourasl, M. Alizadeh, "Numerical solution of Volterra type integral equation of the first kind with wavelet basis", Applied Math. and Comp., Vol. 194, pp. 400-405, 2007 https://doi.org/10.1016/j.amc.2007.04.031
  2. 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 https://doi.org/10.1049/ip-cta:19970702
  3. M. Ohkita and Y. Kobayashi, "An application of rationalized Haar functions to solution of linear differential equations". IEEE Trans. Circuits Systems I. Fundam. Theory Appl. Vol. 9, pp. 853-862, 1986
  4. 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 https://doi.org/10.1109/81.828579
  5. 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 Techn., pp.239-244, 2007
  6. 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 https://doi.org/10.1016/S0045-7906(01)00011-8
  7. A. Haar, "Zur Theorie der orthogonaler Funktionensysteme", Math. Ann. Vol. 69, pp. 331-371, 1910 https://doi.org/10.1007/BF01456326
  8. R.A. Horn and C.R. Johnson, "Matrix Analysis", New York, Cambridge Univ. Press, 1985
  9. J. Brewer, "Kronecker products and matrix calculus in system theory", IEEE Trans. on Circuits and Systems, Vol. 25, pp. 772-781, 1978 https://doi.org/10.1109/TCS.1978.1084534