To determine that all the roots of a transcendental polynomial have negative real parts

Chinese Annals of Mathematics. Series B

Volumn 18, Issue 3, 1997, Pages 373-392

  Hu, Bo ^a,b  

^a SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^b UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Asymptotic stability; Direct analytic method; Transcendental polynomial

Indexed keywords

EID: 25444446814     PISSN: 02529599     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. Avellar, C. E. & Hale, J. K., On the zeros of exponential polynomials, J. Math. Anal. Appl., 73(1980), 434-452.
2. Bellman, R. & Cooke, K. L., Differential-difference equations, Academic Press, New York, 1963.
3. Capyrin, V. N., On the problem of Hurwitz for transcendental equations, Prikl. Mat. Meh., 12 (1948), 301-328.
4. Datko, R., A procedure for determination of the exponential stability of certain differential-difference equations, Quart. Appl. Math., 36 (1978), 279-292.
5. El'sgol'ts, L. E. & Norkin, S. B., Introduction of the theory and application of differential equations with deviating arguments, Academic Press, New York, 1973.
6. Fleming, W., Functions of several variables, Springer-Verlag, New York, 1977.
7. Gantmacher, F. R., Application of the theory of matrices, New York, Interscience, 1959.
8. Hale, J. K., Theory of functional differential equations, Springer-Verlag, New York, 1977.
9. Hale, J. K., Infante, E. F. & Tsen, F. P., Stability in linear delay equations, J. Math. Anal. Appl., 105 (1985), 533-555.
10. Hayes, N. D., Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. Soc., 25 (1950), 226-232.
11. Hu, B., Stabilization of two-dimentional linear systems by time-delay feedback controls, Diff. and Intergral Equ., 9:2(1996), 409-420.
12. Hu, B., Stabilization of two-dimensional linear systems by time-delay feedback controls II, submitted.
13. Kolmanovskii, V. B. & Nosov, V. R., Stability of functional differential equations, Academic Press, London, 1986.
14. Mahaffy, J. M., A test for stability of linear differential delay equations, Quart. Appl. Math., 40 (1982), 193-202.
15. Marden, M., Geometry of polynomials, Math. Surveys, No. 3, Amer. Math. Soc., Providence, RI, 1966.
16. Pontryagin, L. S., On the zeros of some elementary transcendental functions, Amer. Math. Soc. Transi. Ser., 2, 1 (1955), 95-110.
17. Qin Yuanxun, On the equivalence problem of differential equations and difference-differential equations in the theory of stability, Acta Math. Sinica, 10:1(1958), 457-472.
18. Qin Yuanxun, Liou Yongqing & Wang Lian, Motion stability of dynamic systems with time delays, Science Press, Beijing, 1963.
19. Ruan Jiong, Huang Zhengxun & Gao Guozhu, Stability equivalence problem of differential equations and differential-difference equations of neutral type, Acta Math. Sinica, 27:5(1984), 716-720.
20. Thowsen, A., The Routh-Hurwitz method for stability determination of linear differential-difference systems, Int. J. Control, 33:5(1981), 991-995.
21. Thowsen, A., An analytic stability test for a class of time-delay systems, IEEE Trans. Automat. Contr., AC-26:3(1981), 735-736.
22. Yong, J., Stabilization of linear systems by time-delay feedback controls, Quart. Appl. Math.,45(1987), 371-388.
23. Yong, J., Stabilization of linear systems by time-delay feedback controls II, Quart. Appl. Math.,46(1988), 593-603.