미소구간 유리하알변환에 의한 선형계의 해석을 위한 새로운 접근방법

New Approach to the Analysis of Linear Systems Via Local Rationalized Haar Transform

  • 김진태 (성균관대 전기전자 및 컴퓨터 공학과) ;
  • 안두수 (성균관대 전기전자 및 컴퓨터 공학과)
  • 발행 : 2002.06.01

초록

This paper proposes a real-time application of rationalized Haar transform which is based on the local rationalized Haar transform, local operational matrix and local delay operational matrix. This approach let a general sampling time be used by introducing a scaling factor. In the existing method of orthogonal functions, a major disadvantage is that process signals need to be recorded prior to obtaining their expansions. This paper proposes a novel method of rationalized Haar transform to overcome this shortcoming. And the proposed method is suitable for the analysis of linear systems. The proposed method is expected to the applicable to the adaptive control which demanded to the real-time applications.

키워드

참고문헌

  1. Alfred Haar, 'Zur theorie der orthogonalen funktonen systeme', Mathematische Annalen, 69:331-371, 1910 https://doi.org/10.1007/BF01456326
  2. J. E. Shore, 'On the applications of Haar functions', IEEE Trans. Communication, vol.21, 209-216, 1973 https://doi.org/10.1109/TCOM.1973.1091637
  3. P. R. Roeser and M. E. Jernigan, 'Fast Haar transform algorithms', IEEE Trans. Computers, vol. C-31, no2, 175-177, 1982 https://doi.org/10.1109/TC.1982.1675965
  4. M. Ohkita and Y. Kobayashi and M. Ionue, 'Application of Haar functions to solution of differential equations', Mathematics and Computers in Simulation, 25(1), 31-38, 1983 https://doi.org/10.1016/0378-4754(83)90027-7
  5. M. Ohkita and Y. Kobayashi, 'An application of rationalized Haar functions to solution of linear differential equations', IEEE Trans. Circuits and Systems, 33(9), 853-862, 1986 https://doi.org/10.1109/TCS.1986.1086019
  6. M. Ohkita, 'An application of rationalized Haar functions to the solution of delay-differential systems', Mathematics and Computers in Simulation, 29(6), 447-491, 1987 https://doi.org/10.1016/0378-4754(87)90083-8
  7. Albansei. M. G. and Ferretti. M., 'A high speed Haar transform implementation', J. Circuit Syst. Computer, vol/2, no3, 207-226, 1992 https://doi.org/10.1142/S0218126692000143
  8. Kanti B Datta and B M Mohan, Orthogonal Functions in Systems and Control, World Scientific Publishing, 1995
  9. J. L. Atsushi Watanabe and Seiichi Kawata, 'On operational matrices of Walsh functions', Proc. American Control Conference Albuquerque, 2272-2277, 1997 https://doi.org/10.1109/ACC.1997.609005
  10. 안두수, WALSH함수와 시스템 제어, 복두출판산, 2000
  11. 김진태, 김태훈, 이명규, 안두수, '월쉬함수에 의한 비선형계의 해석 및 최적제어에 관한 연구', 대한전기학회논문집, 제49D권, 7호, 354-362, 2000