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Boundedness of the solutions of impulsive differential systems with time-varying delay. (English) Zbl 1062.34091

The authors investigate the boundedness of the solutions of impulsive functional-differential equations with time-varying delay. The main results are obtained by using Lyapunov functions and Razumikhin technique.

MSC:

34K45 Functional-differential equations with impulses
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References:

[1] Shen, J.; Yan, J., Razumikhin type stability theorems for impulsive functional differential equations, Nonlinear Anal., 33, 519-531 (1998) · Zbl 0933.34083
[2] Yang, T., Impulsive Systems and Control: Theory and Applications (2001), Nova Science Publishers: Nova Science Publishers Huntington, New York · Zbl 0990.00035
[3] Luo, Z.; Shen, J., New Razumikhin type theorems for impulsive functional differential equations, Appl. Math. Comput., 125, 375-386 (2002) · Zbl 1030.34078
[4] Shen, J. H., Existence and uniqueness of solutions for impulsive functional differential equations on the PC space with applications, Acta Sci. Nat. Univ. Norm. Hunan, 19, 13-17 (1996)
[5] Sun, J. T.; Zhang, Y. P.; Wu, Q. D., Impulsive control for the stabilization and synchronization of Lorenz systems, Phys. Lett. A, 298, 153-160 (2002) · Zbl 0995.37021
[6] Shen, J. H., Razumikhin techniques in impulsive functional differential equations, Nonlinear Anal., 36, 119-130 (1999) · Zbl 0939.34071
[7] Sun, J. T.; Zhang, Y. P.; Wu, Q. D., Less conservative conditions for asymptotic stability of impulsive control systems, IEEE Trans. Automat. Contr., 48, 829-831 (2003) · Zbl 1364.93691
[8] Ballinger, G.; Liu, X., Existence and uniqueness results for impulsive delay differential equations, DCDIS, 5, 579-591 (1999) · Zbl 0955.34068
[9] Hristova, S. G.; Roberts, L. F., Razumikhin technique for boundedness of the solutions of impulsive integrodifferential equations, Math. Comput. Model., 34, 839-847 (2001) · Zbl 1045.45004
[10] Yu, J. S.; Zhang, B. G., Stability theorems for delay differential equations with impulses, J. Math. Anal. Appl., 198, 285-297 (1996) · Zbl 0853.34068
[11] Sun, J. T.; Zhang, Y. P.; Wang, L.; Wu, Q. D., Impulsive robust control of uncertain Lur’e systems, Phys. Lett. A, 304, 130-135 (2002) · Zbl 1001.93071
[12] Liu, X. Z.; Ballinger, G., Uniform asymptotic stability of impulsive delay differential equations, Comput. Math. Appl., 41, 903-915 (2001) · Zbl 0989.34061
[13] Bainov, D. D.; Simeonov, P. S., Systems with impulse effect, (Stability Theory and Applications (1989), Ellis Horwood: Ellis Horwood Chichester, UK) · Zbl 0661.34060
[14] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[15] Soliman, A. A., On stability of impulsive differential systems, Appl. Math. Comput., 133, 105-117 (2002) · Zbl 1030.34043
[16] Soliman, A. A., Stability criteria of perturbed impulsive differential systems, Appl. Math. Comput., 134, 445-457 (2003) · Zbl 1030.34046
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