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Practical stability of impulsive functional differential equations in terms of two measurements. (English) Zbl 1075.34083

The authors investigate the practical stability of the solutions of an impulsive functional-differential equation. The main results are obtained by using Lyapunov functions coupled with Razumikhin technique.

MSC:

34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
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References:

[1] Lakshmikantham, V.; Bainov, D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific New York · Zbl 0719.34002
[2] Yang, T., Impulsive systems and control: theory and applications, (2001), Nova Science Publishers Singapore
[3] Ken, C.H.; Zhang, S.N., Practical stability for finite delay differential systems in terms of two measures, Acta mathematicae applicatae sinica, 25, 3, (2002)
[4] Sun, J.T.; Zhang, Y.P.; Wang, L.; Wu, Q.D., Impulsive robust control of uncertain Lur’e systems, Phys. letters A, 304, 130-135, (2002) · Zbl 1001.93071
[5] Soliman, A.A., On stability of impulsive differential systems, Appl. math. computation, 133, 105-117, (2002) · Zbl 1030.34043
[6] Soliman, A.A., Stability criteria of perturbed impulsive differential systems, Appl. math. computation, 134, 445-457, (2003) · Zbl 1030.34046
[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, 5, 829-831, (2003) · Zbl 1364.93691
[8] Sun, J.T.; Zhang, Y.P., Impulsive control of a nuclear spin generator, J. of computational and applied mathematics, 157, 1, 235-242, (2003) · Zbl 1051.93086
[9] Bainov, D.D.; Stamova, I.M., On the practical stability of the solutions of impulsive systems of differentialdifference equations with variable impulsive perturbations, Journal of mathematical analysis and applications, 200, 272-288, (1996) · Zbl 0848.34058
[10] Shen, J.H., Razumikhin techniques in impulsive functional differential equations, Nonlinear analysis, 36, 119-130, (1999) · Zbl 0939.34071
[11] Liu, X.Z.; Ballinger, G., Uniform asymptotic stability of impulsive delay differential equations, Computers math. applic., 41, 7/8, 903-915, (2001) · Zbl 0989.34061
[12] Hristova, S.G.; Roberts, L.F., Razumikhin technique for boundedness of the solutions of impulsive integrodifferential equations, Mathl. comput. modelling, 34, 7/8, 839-847, (2001) · Zbl 1045.45004
[13] Stamov, G.T.; Stamova, I.M., Second method of Lyapunov and existence of integral manifolds for impulsive differential-difference equations, Journal of mathematical analysis and applications, 258, 371-379, (2001) · Zbl 0982.34068
[14] Martynyuk, A.A., Practical stability conditions for hybrid systems, (), 344-347
[15] Lakshmikantham, V.; Leela, S.; Martynyuk, A.A., Practical stability of nonlinear systems, (1990), World Scientific Huntington, New York · Zbl 0753.34037
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