91
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Generalised resultants, dynamic polynomial combinants and the minimal design problem

Pages 1946-1964 | Received 26 Jan 2013, Accepted 27 Mar 2013, Published online: 20 Aug 2013

References

  • Barnett , S. Greatest common divisor of several polynomials . 263 – 268 .
  • Brockett , R. W. and Byrnes , C. I. 1981 . Multivariable nyquist criterion, root loci and pole placement: Ageometric viewpoint . IEEE Transactions on Automatic Control , AC-26 : 271 – 283 . doi: 10.1109/TAC.1981.1102571
  • Fatouros , S. and Karcanias , N. 2003 . Resultant properties of GCD of many polynomials and a factorisation representation of GCD . International Journal of Control , 76 : 1666 – 1683 . doi: 10.1080/00207170310001628598
  • Hermann , R. and Martin , C. 1975 . Applications of algebraic geometry to systems theory—part 1 . IEEE Transactions on Automatic Control , 22 : 19 – 25 . doi: 10.1109/TAC.1977.1101395
  • Hodge , W. V.D. and Pedoe , P. D. 1952 . Methods of algebraic geometry , Cambridge University Press . ). Cambridge:
  • Kailath , T. 1980 . Linear systems , Englewood Cliffs , NJ : Prentice Hall .
  • Karcanias , N. 1987 . Invariance properties, and characterization of the greatest common divisor of a set of polynomials . International Journal of Control , 46 : 1751 – 1760 . doi: 10.1080/00207178708934007
  • Karcanias , N. The minimal design problem on dynamic polynomial combinants in . Proceedings of 18th IFAC World Congress , , 28 Aug–2 Sept 2011
  • Karcanias , N. and Galanis , G. 2010 . Dynamic polynomial combinants and generalised resultants . Bulletin of Greek Math Society , 57 : 229 – 250 .
  • Karcanias , N. and Giannakopoulos , C. 1984 . Grassmann invariants, almost zeros and the determinantal pole-zero assignment problems of linear systems . International Journal of Control , 40 : 673 – 698 . doi: 10.1080/00207178408933300
  • Karcanias , N. , Giannakopoulos , C. and Hubbard , M. 1983 . Almost zeros of a set of polynomials of . International Journal of Control , 38 : 1213 – 1238 . doi: 10.1080/00207178308933141
  • Karcanias , N. , Mitrouli , M. , Fatouros , S. and Halikias , G. 2006 . Approximate GCD of many polynomials, generalised resultants and strength of approximation . Computers and Mathematics with Applications , 51 : 817 – 1830 . doi: 10.1016/j.camwa.2006.01.010
  • Kucera , V. 1979 . Discrete linear control: The polynomial equation approach , New York : John Wiley & Sons .
  • Leventides , L. and Karcanias , N. 1992 . A new sufficient condition for arbitrary pole placement by real constant output feedback . Systems and Control Letters , 3 : 191 – 200 . doi: 10.1016/0167-6911(92)90005-D
  • Leventides , J. and Karcanias , N. 1995 . Global asymptotic linearisation of the pole placement map: A closed form solution of the output feedback problem . Automatica , 31 : 1303 – 1309 . doi: 10.1016/0005-1098(95)00047-Z
  • Leventides , J. and Karcanias , N. 1998 . Dynamic pole assignment using global, blow up linearisation: Low complexity solutions . Journal of Optimisation Theory and Applications , 96 : 57 – 86 . doi: 10.1023/A:1022659032574
  • Marcus , M. 1973 . Finite dimensional multilinear algebra (Parts 1 and 2) , New York : Marcel Dekker .
  • Marcus , M. and Minc , M. 1964 . A survey of matrix theory and matrix inequalities , Boston : Allyn and Bacon .
  • Shan , X. Y. and Karcanias , N. 1994 . Pole mobility and minimal norm stabilization of SISO systems under bounded state feedback . International Journal of Control , 60 : 1137 – 1162 . doi: 10.1080/00207179408921515
  • Vardulakis , A. I.G. and Stoyle , P. N.R. 1978 . Generalised resultant theorem . Journal of IMA , 22 : 331 – 335 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.