International Journal of Control, Automation, and Systems

  • 제2권3호
  • /
  • Pages.319-332
  • /
  • 2004
  • /
  • 1598-6446(pISSN)
  • /
  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

Further Improvements on Bose's 2D Stability Test

  • Xu, Li (Faculty of System Science and Technology, Akita Prefecture University) ;
  • Yamada, Minoru (Gifu National College of Technolog) ;
  • Lin, Zhiping (Nanyang Technological University) ;
  • Saito, Osami (Chiba University) ;
  • Anazawa, Yoshihisa (Faculty of System Science and Technology, Akita Prefecture University)
  • 발행 : 2004.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper proposes some further improvements on N.K. Bose's 2D stability test for polynomials with real coefficients by revealing symmetric properties of the polynomials, resultants occurring in the test and by generalizing Sturm's method. The improved test can be fulfilled by a totally algebraic algorithm with a finite number of steps and the computational complexity is largely reduced as it involves only certain real variable polynomials with degrees not exceeding half of their previous complex variable counterparts. Nontrivial examples for 2D polynomials having both numerical and literal coefficients are also shown to illustrate the computational advantage of the proposed method.

키워드

참고문헌

  1. IEEE Trans. on Acoustics, Speech and Signal Processing v.25 Implementation of a new stability test for two-dimensional filters N. K. Bose https://doi.org/10.1109/TASSP.1977.1162917
  2. Journal of the Franklin Institute v.330 no.5 Simplification of a multidimensional digital filter stability test N. K. Bose https://doi.org/10.1016/0016-0032(93)90084-8
  3. Multidimensional Systems: Techniques and Applications Stability of multidimensional systems and related problems E. I. Jury;S.G. Tzafestas(ed.)
  4. IEEE Trans. on Circuits and Systems v.34 no.10 New results on stable multidimensional polynomials - Part I: Continuous case A. Fettweis;S. Basu https://doi.org/10.1109/TCS.1987.1086057
  5. IEEE Trans. on Circuits and Systems v.34 New results on stable multidimensional polynomials - Part II: Discrete cases S. Basu;A. Fettweis
  6. IEEE Trans. on Circuits and Systems v.38 no.7 New results on stable multidimensional polynomials - Part III: State-space interpretations S. Basu https://doi.org/10.1109/31.135747
  7. IEEE Trans. on Circuits and Systems-II: Analog and Digital Signal Processing v.41 On two-dimensional filter stability test X. H. Hu;E. I. Jury https://doi.org/10.1109/82.298377
  8. Multidimensional Systems and Signal Processing v.13 no.1 Stability testing of two-dimensional discrete-time systems by a scattering-type stability table and its telepolation Y. Bistritz https://doi.org/10.1023/A:1013843411523
  9. IEEE Trans. on Audio Electroacoust v.20 Stability of two-dimensional recursive filters T. S. Huang https://doi.org/10.1109/TAU.1972.1162364
  10. IEEE Trans. on Acoustics, Speech and Signal Processing v.25 Some new results on discrete system stability J. Szczupak;S. K. Mitra;E. J. Jury https://doi.org/10.1109/TASSP.1977.1162896
  11. IEEE Trans. on Automatic Control v.48 no.4 A new approach to digital pid controller design L. H. Keel;J. I. Rego;S. P. Bhattacharyya https://doi.org/10.1109/TAC.2003.809768
  12. Proc. of CCA99 Development of n D control system toolbox for use with MATLAB L. Xu;M. Yamada;O. Saito
  13. IEEE Trans. on Acoustics, Speech and Signal Processing v.24 no.1 A stability theorem for discrete systems H. W. Schussler https://doi.org/10.1109/TASSP.1976.1162762
  14. IEEE Trans. on Acoustics, Speech and Signal Processing v.ASSP-29 A note on the new 1-D and 2-D stability theorems for discrete systems R. Gnanasekaran
  15. IEEE Trans. on Circuits and Systems v.38 2-D filter stability test using polynomial array for $F(z_1,z_2)$ on |$z_1$|=1 X. H. Hu https://doi.org/10.1109/31.83882
  16. Synthesis of Passive Networks E. A. Guillemin
  17. Lecture of Algebra (in Japanese) T. Takagi
  18. IEEE Trans. on Circuits and Systems-II: Analog and Digital Signal Processing v.42 no.10 A fast 2-D stability test procedure based on fft and its computational complexity K. Kurosawa;I. Yamada;T. Yokokawa https://doi.org/10.1109/82.471397
  19. IEEE Trans. on Circuits and Systems-II v.50 no.9 Comments on 'stability tests of N-dimensional discrete time systems using polynomial arrays' L. Xu;J. Ying;Z. Lin;O. Saito https://doi.org/10.1109/TCSII.2003.816934