|
Delay-dependent and delay-independent stability criteria for a delay differential system
Author(s):
Hideaki
Matsunaga
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4305-4312.
MSC (2000):
Primary 34K20;
Secondary 34K25
Posted:
June 30, 2008
MathSciNet review:
2431044
Retrieve article in:
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:
-
- 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
Email:
hideaki@ms.osakafu-u.ac.jp
DOI:
10.1090/S0002-9939-08-09396-9
PII:
S 0002-9939(08)09396-9
Keywords:
Asymptotic stability,
stability criteria,
delay differential equations,
characteristic equation
Received by editor(s):
October 19, 2007
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
