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Strict stability of impulsive functional differential equations. (English) Zbl 1068.34073
The authors apply Lyapunov functionals and Razumikhin technique to prove some results on strict uniform stability or Lyapunov’s uniform asymptotic stability of the trivial solution of a retarded functional-differential equation with fixed times of impulsive effects.

MSC:
34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
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[1] Lakshmikantham, V.; Mohapatra, R.N., Strict stability of differential equations, Nonlinear anal., 46, 915-921, (2001) · Zbl 1008.34041
[2] Lakshmikantham, V.; Zhang, Y., Strict practical stability of delay differential equation, Appl. math. comput., 118, 275-285, (2001) · Zbl 1035.34082
[3] Shen, J.H., Razumikhin techniques in impulsive functional differential equations, Nonlinear anal., 36, 119-130, (1999) · Zbl 0939.34071
[4] Yang, T., Impulsive systems and control: theory and applications, (2001), Nova Science Huntington, NY
[5] Shen, J.H.; Luo, Z.G.; Liu, X.Z., Impulsive stabilization of functional differential equations via Liapunov functionals, J. math. anal. appl., 240, 1-15, (1999)
[6] Yan, J.R.; Kou, C.H., Oscillation of solutions of impulsive delay differential equations, J. math. anal. appl., 254, 358-370, (2001) · Zbl 0981.34076
[7] Yan, J.R., Oscillation of nonlinear delay impulsive differential equations and inequalities, J. math. anal. appl., 265, 332-342, (2002) · Zbl 1001.34059
[8] Sun, J.T.; Zhang, Y.P.; Wu, Q.D., Less conservative conditions for asymptotic stability of impulsive control systems, IEEE trans. automat. control, 48, 829-831, (2003) · Zbl 1364.93691
[9] Zhang, Y.; Sun, J.T., Boundedness of the solutions of impulsive differential systems with time-varying delay, Appl. math. comput., 154, 279-288, (2004) · Zbl 1062.34091
[10] Sun, J.T., Stability criteria of impulsive differential system, Appl. math. comput., 156, 1, 85-91, (2004) · Zbl 1062.34006
[11] Sun, J.T.; Zhang, Y.P., Stability analysis of impulsive control systems, IEE proc. control theory appl., 150, 331-334, (2003)
[12] Zhang, S.N., A new technique in stability of infinite delay differential equations, Comput. math. appl., 44, 1275-1287, (2002) · Zbl 1072.34082
[13] Li, Z.G.; Soh, C.B.; Xu, X.H., Stability of impulsive differential systems, J. math. anal. appl., 216, 644-653, (1997) · Zbl 0899.34010
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