Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Delay-dependent and delay-independent stability criteria for a delay differential system

Author: Hideaki Matsunaga
Journal: Proc. Amer. Math. Soc. 136 (2008), 4305-4312
MSC (2000): Primary 34K20; Secondary 34K25
Published electronically: June 30, 2008
MathSciNet review: 2431044
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a linear delay differential system with two coefficients and one delay, we establish some necessary and sufficient conditions on the asymptotic stability of the zero solution, which are composed of delay-dependent and delay-independent stability criteria. On the former criterion, the range of the delay is explicitly given.

References [Enhancements On Off] (What's this?)

  • 1. K. L. Cooke and P. van den Driessche, On zeroes of some transcendental equations, Funkcial. Ekvac., 29 (1986), 77-90. MR 865215 (87m:34098)
  • 2. K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl., 86 (1982), 592-627. MR 652197 (84b:34107)
  • 3. H. I. Freedman and Y. Kuang, Stability switches in linear scalar neutral delay equations, Funkcial. Ekvac., 34 (1991), 187-209. MR 1130459 (92m:34183)
  • 4. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993. MR 1243878 (94m:34169)
  • 5. T. Hara and J. Sugie, Stability region for systems of differential-difference equations, Funkcial. Ekvac., 39 (1996), 69-86. MR 1401653 (97c:34154)
  • 6. N. D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. Soc., 25 (1950), 226-232. MR 0036426 (12:106d)
  • 7. J. Hofbauer and J. W.-H. So, Diagonal dominance and harmless off-diagonal delays, Proc. Amer. Math. Soc., 128 (2000), 2675-2682. MR 1707519 (2000m:34171)
  • 8. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993. MR 1218880 (94f:34001)
  • 9. H. Matsunaga, Exact stability criteria for delay differential and difference equations, Appl. Math. Lett., 20 (2007), 183-188. MR 2283908 (2007k:34258)
  • 10. S. Sakata, Asymptotic stability for a linear system of differential-difference equations, Funkcial. Ekvac., 41 (1998), 435-449. MR 1676882 (2000a:34156)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34K20, 34K25

Retrieve articles in all journals with MSC (2000): 34K20, 34K25

Additional Information

Hideaki Matsunaga
Affiliation: Department of Mathematical Sciences, Osaka Prefecture University, Sakai 599-8531, Japan

Keywords: Asymptotic stability, stability criteria, delay differential equations, characteristic equation
Received by editor(s): October 19, 2007
Published electronically: June 30, 2008
Additional Notes: This work was supported in part by Grant-in-Aid for Young Scientists (B), No. 19740071, of the Japanese Ministry of Education, Culture, Sports, Science and Technology.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society