Stability of impulsive infinite delay differential equations. (English) Zbl 1125.34345

Using new Lyapunov functions technique developed by Shunian Zhang the authors study the stability for impulsive differential equations with infinite delays. Some known results are improved.


34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
Full Text: DOI


[1] Zhang, S. N., A new technique in stability of infinite delay differential equations, Comput. Math. Appl., 44, 1275-1287 (2002) · Zbl 1072.34082
[2] Yang, T., Impulsive control, IEEE Trans. Automat. Control, 44, 1081-1083 (1999) · Zbl 0954.49022
[3] Yang, T., Impulsive Systems and Control: Theory and Applications (2001), Nova Science Publishers, Inc.: Nova Science Publishers, Inc. Huntington, NY · Zbl 0970.00011
[4] Shen, J. H., Razumikhin techniques in impulsive functional differential equations, Nonlinear Anal., 36, 119-130 (1999) · Zbl 0939.34071
[5] Liu, X. Z.; Ballinger, G., Uniform asymptotic stability of impulsive delay differential equations, Comput. Math. Appl., 41, 903-915 (2001) · Zbl 0989.34061
[6] Luo, Z. G.; Shen, J. H., New Razumikhin type theorems for impulsive functional differential equations, Appl. Math. Comput., 125, 375-386 (2002) · Zbl 1030.34078
[7] Soliman, A. A., Stability criteria of impulsive differential systems, Appl. Math. Comput., 134, 445-457 (2003) · Zbl 1030.34046
[8] Sun, J. T.; Zhang, Y. P., Stability analysis of impulsive control systems, IEEE Proc. Control Theory Appl., 150, 4, 331-334 (2003)
[9] Sun, J. T.; Zhang, Y. P., Impulsive control of a nuclear spin generator, J. Comput. Appl. Math., 157, 1, 235-242 (2003) · Zbl 1051.93086
[10] Zhang, Y.; Sun, J. T., Boundedness of the solutions of impulsive differential systems with time-varying delay, Appl. Math. Comput., 154, 1, 279-288 (2004) · Zbl 1062.34091
[11] Sun, J. T.; Zhang, Y. P.; Wu, Q. D., Less conservative conditions for asymptotic stability of impulsive control systems, IEEE Trans. Automat. Control, 48, 5, 829-831 (2003) · Zbl 1364.93691
[12] Kou, C. H.; Zhang, S. N.; Wu, S. J., Stability analysis in terms of two measures for impulsive differential equations, J. London Math. Soc., 66, 1, 142-152 (2002) · Zbl 1026.34013
[13] Cuevas, C.; Pinto, M., Asymptotic properties of solutions to nonautonomous Volterra difference systems with infinite delay, Comput. Math. Appl., 42, 3-5, 671-685 (2001) · Zbl 1002.39007
[14] Liang, J.; Xiao, T. J.; van Casteren, J., A note on semilinear abstract functional differential and integrodifferential equations with infinite delay, Appl. Math. Lett., 17, 4, 473-477 (2004) · Zbl 1082.34543
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