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

Matsunaga, Hideaki

doi:10.1090/S0002-9939-08-09396-9

Delay-dependent and delay-independent stability criteria for a delay differential system
HTML articles powered by AMS MathViewer

by Hideaki Matsunaga PDF

Proc. Amer. Math. Soc. 136 (2008), 4305-4312 Request permission

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

Kenneth L. Cooke and Pauline van den Driessche, On zeroes of some transcendental equations, Funkcial. Ekvac. 29 (1986), no. 1, 77–90. MR 865215
Kenneth L. Cooke and Zvi Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl. 86 (1982), no. 2, 592–627. MR 652197, DOI 10.1016/0022-247X(82)90243-8
H. I. Freedman and Y. Kuang, Stability switches in linear scalar neutral delay equations, Funkcial. Ekvac. 34 (1991), no. 2, 187–209. MR 1130459
Jack K. Hale and Sjoerd M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, vol. 99, Springer-Verlag, New York, 1993. MR 1243878, DOI 10.1007/978-1-4612-4342-7
Tadayuki Hara and Jitsuro Sugie, Stability region for systems of differential-difference equations, Funkcial. Ekvac. 39 (1996), no. 1, 69–86. MR 1401653
N. D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation, J. London Math. Soc. 25 (1950), 226–232. MR 36426, DOI 10.1112/jlms/s1-25.3.226
Josef Hofbauer and Joseph W.-H. So, Diagonal dominance and harmless off-diagonal delays, Proc. Amer. Math. Soc. 128 (2000), no. 9, 2675–2682. MR 1707519, DOI 10.1090/S0002-9939-00-05564-7
Yang Kuang, Delay differential equations with applications in population dynamics, Mathematics in Science and Engineering, vol. 191, Academic Press, Inc., Boston, MA, 1993. MR 1218880
Hideaki Matsunaga, Exact stability criteria for delay differential and difference equations, Appl. Math. Lett. 20 (2007), no. 2, 183–188. MR 2283908, DOI 10.1016/j.aml.2006.03.012
Sadahisa Sakata, Asymptotic stability for a linear system of differential-difference equations, Funkcial. Ekvac. 41 (1998), no. 3, 435–449. MR 1676882