Eventual practical stability of impulsive differential equations with time delay in terms of two measurements. (English) Zbl 1063.34070

Summary: We introduce a new stability – eventual practical stability for impulsive differential equations with time delay. By using Lyapunov functions and comparison principle, we obtain some criteria of eventual practical stability, eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements.


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


[1] Bainov, D.D.; Stamova, I.M., On the practical stability of the solutions of impulsive systems of differential-difference equations with variable impulsive perturbations, J. math. anal. appl., 200, 272-288, (1996) · Zbl 0848.34058
[2] Kou, C.H.; Zhang, S.N., Practical stability for finite delay differential systems in terms of two measures, Acta math. appl. sinica, 25, 3, 476-483, (2002) · Zbl 1049.34092
[3] Lakshmikantham, V.; Matrosov, V.M.; Sivasundaram, S., Vector Lyapunov functions and stability analysis of nonlinear systems, (1991), Kluwer Academic Dordrecht · Zbl 0721.34054
[4] 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
[5] Soliman, A.A., Stability criteria of impulsive differential systems, Appl. math. comput., 134, 445-457, (2003) · Zbl 1030.34046
[6] J.T. Sun, Stability criteria of impulsive differential system, Appl. Math. Comput. 156 (2004) 85-91. · Zbl 1062.34006
[7] 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
[8] Sun, J.T.; Zhang, Y.P., Stability analysis of impulsive control systems, IEE proc. control theory appl., 150, 4, 331-334, (2003)
[9] 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
[10] Yang, T., Impulsive systems and controltheory and applications, (2001), Nova Science Publishers Huntington NY
[11] Yu, J.S., Stability for nonlinear delay differential equations of unstable type under impulsive perturbations, Appl. math. lett., 14, 849-857, (2001) · Zbl 0992.34055
[12] 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.