DOI QR코드

DOI QR Code

Schur Stability of Complex Polynomials

복소다항식의 Schur 안정성

  • 추연석 (홍익대학교 전자전기공학과) ;
  • 김동민 (홍익대학교 전자전기공학과)
  • Published : 2009.07.01

Abstract

Determining the Schur stability of a polynomial is one of fundamental steps in many engineering problems including digital control system design or digital filter design. Due to its importance a variety of techniques have been reported in the literature for checking the Schur stability of a given polynomial. However most of them focus on real polynomials, and few results are available for complex polynomials. This paper concerns the Schur stability of complex polynomials. A simplified Jury's table for real polynomials is extended to complex polynomials.

References

  1. E. I. Jury, Theory and Application of the z-Transform Method,Wiley, New York, 1964
  2. X. Hu, 'On the schur-cohn minors and inner determinants and a new stability table,' J Franldin Inst., vol. 331B, no. 1, pp. 1-11, 1994 https://doi.org/10.1016/0016-0032(94)90074-4
  3. G A. Maria and M. M. Fahmy, 'On the stability of twodimensional digital filters,' IEEE Trans. Audio Electroacoust., vol.21,no.1,pp.470-472,1973 https://doi.org/10.1109/TAU.1973.1162511
  4. E.I. Jury, 'Modified stability table for 2-D digital filters,' IEEE Trans. Circuits Syst., vol. 35, no. 1, pp. 116-119, 1988 https://doi.org/10.1109/31.1707
  5. Y. Bistritz, 'A cirsulat stability test for general polynomials,' Systems Control Lett., vol. 7, pp. 89-97, 1986 https://doi.org/10.1016/0167-6911(86)90013-7
  6. Y. Bistritz, 'Immitance-type tabular stability test for 2-D LSI systems based on a zero location test for I-D complex polynomials,' Circuits systems Signal Process., vol. 19, pp. 245-265,2000 https://doi.org/10.1007/BF01204577
  7. R. H. Raible, 'A simplification of Jury's tabular form,' IEEE Trans. Automat. Contr., vol. 19, pp. 248-250,1974 https://doi.org/10.1109/TAC.1974.1100574
  8. K. J. Astrom, Introduction to stochastic control theory, Academic Press, New York, 1970
  9. T. Mori and H. Kokame, 'Single-parameter characterizations of Schur stability,' IEICE Trans., vol. E84-A, no. 8, pp. 2061-2064, 2001
  10. H. Chapellat, M. Mansour, and S. P. Bhattacharyya, 'Elementary proofs of some classical stability criteria,' IEEE Trans. Educ., vol. 33, no. 3, pp. 232-239, 1990 https://doi.org/10.1109/13.57067
  11. D. Goodman, 'Some stability properties of two-dimensional linear shift-invariant digital filters,' IEEE Trans. Circuits Syst., vol. 24, no.4, pp. 201-208, 1977 https://doi.org/10.1109/TCS.1977.1084322
  12. T. S. Huang, 'Stability of two-dimensional recursive filters,' IEEE Trans. Audio Electroacoust., vol. 20, no. 2, pp. 158-163, 1972 https://doi.org/10.1109/TAU.1972.1162364
  13. L. Xu, Z. Lin, O. Saito, and Y. Anazawa, 'Further improvements on Bose's 2D stability test,' Int. J Control Automation Sys., vol. 2, no. 3, pp. 319-332, 2004