Network Realizability Theory Approach to Stability of Complex Polynomials

IEEE Transactions on Circuits and Systems

Volumn 34, Issue 2, 1987, Pages 216-218

  Bose, N K ^a   Shi, Y Q ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC FILTERS - THEORY; MATHEMATICAL TECHNIQUES - POLYNOMIALS;

HURWITZ POLYNOMIALS; MULTIDIMENSIONAL FILTERS; MULTIVARIATE POLYNOMIALS;

SYSTEM STABILITY;

EID: 0023293754     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCS.1987.1086097     Document Type: Article

References (20)

1. J. W. Rogers, “Location of roots of polynomials,” SIAM Rev., vol. 25, no. 3, pp. 327–342, July 1983.
2. S. D. Agashe, “A new general Routh-like algorithm to determine the number of RHP roots of a real or complex polynomial,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 406–409, Apr. 1985.
3. X. K. Xie, “Stable polynomials with complex coefficients,” in Proc. 24th IEEE Conf. Decision Contr., (Fort Lauderdale, FL), Dec. 1985, pp. 324–325.
4. T. H. Crystal and L. Ehrman, “The design and application of digital filters with complex coefficients,” IEEE Trans. Audio Electroacoust., vol. 16, pp. 315–320, 1968.
5. R. Boite and H. Leich, “On digital filters with complex coefficients,” in Proc. NA TO Advanced Study Inst. Network and Syst. Theory, Sept. 1972, pp. 344–351.
6. Y. Baba, K. Imamura, and S. Takahashi, “Design of two-dimensional digital filters with complex coefficients,” Electron. Commun. Engineers Japan, vol. J67-A, no. 2, pp. 95–102, 1984.
7. Y. Ichikawa and S. Takahashi, “Some design methods of two-dimensional digital filters with complex coefficients in consideration of linear phase characteristics,” Electron. Commun. Engineers Japan, vol. J67-A, no. 6, pp. 604–611, 1984.
8. G. C. Temes and J. W. Lapatra, Introduction to Circuit Synthesis and Design. New York: McGraw-Hill, 1977.
9. N. K. Bose and R. W. Newcomb, “Tellegen’s theorem and multivariable realizability theory,” Int. J. Electron., vol. 36, pp. 417–425, 1974.
10. S. Barnett, Polynomials and Linear Control Systems. New York: Marcel Dekker, 1983.
11. N. K. Bose, Digital Filters: Theory and Applications. New York: North-Holland Elsevier, 1985.
12. M. Marden, Geometry of Polynomials. Providence, RI: American Math. Society, 1966.
13. A. Fettweis, “Some properties of scattering Hurwitz polynomials,” Arch. Elek. Ubertragung, vol. 38, no. 3, pp. 171–176, 1984.
14. S. Basu and A. Fettweis, “Test for two-dimensional scattering Hurwitz polynomials,” Circuits, Systems Signal Process., vol. 3, no. 2, pp. 226–242, 1984.
15. N. K. Bose, Applied Multidimensional Systems Theory. New York: Van Nostrand Reinhold, 1982.
16. W. C. Karl, “Geometry of vibrational system stability domains with application to control,” M.S. thesis. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 1984.
17. V. L. Kharitonov, “On generalization of a stability criterion” (in Russian), Izv. Akad. Nauk. Kazakh. SSR, Ser. Fiz-Mat, no. 1, pp. 53–57, 1978.
18. N. K. Bose, Multidimensional Systems: Progress, Directions and Open Problems. Dordrecht, Holland: D. Reidel, 1985, pp. 256–258.
19. V. Belevitch, Classical Network Theory. San Francisco: Holden-Day, 1968.
20. N. K. Bose and Y. Q. Shi, “A simple general proof of Kharitonov’s generalized stability criterion,” to be published.