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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 30 | Number 2 | Year 2016 | Article Id. IJMTT-V30P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V30P518

Stability of Impulsive Functional Differential Equations via Lyapunov Functionals


Sanjay K. Srivastava, Neha Wadhwa, Neeti Bhandari
Abstract

In this paper, we consider the impulsive stabilization problems for a class of impulsive functional differential equation of the form Our method is based on the application of the Liapunov second method together with Liapunov functionals.

Keywords
stability, impulsive differential equation, Liapunov functional.
References

[1] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, ‘’Theory of Impulse Differential Equations, ’’World Scientific, Singapore 1989.
[2] D.D. Bainov, P.S. Simeonov, ‘’Systems with Impulse Effect: Stability Theory and Applications,’’ Horwood, Chicestar, 1989.
[3] V. Lakshmikantham and X. Liu, On quasi stability for impulsive differential systems, Nonlinear Anal. 13(1989), 819-828.
[3] J. Shen, Z. Luo, Impulsive stabilization of functional differential equations via Liapunov functionals, J. Math. Anal.Appl. 240 (1999) 1–15.
[4] Katsumasa Kobayashi, Stability Theorems for Functional Differential Equations, Nonlinear Analysis, Theory. Methods & Applicorions, Vol. 20, No. 10, pp. 1183-I 192, 1993.
[5] Burton T. & Hatvani L., Stability theorems for nonautonomous functional differential equations by Liapunov functionals, Tokoku math. J. 41, 65-104 (1989).
[6] Lakshmikantham V., Leela S. & Sivasundaram S., Lyapunov functions on product spaces and stability theory of delay differential equations, J. math. Analysis Applic. 154, 391-402 (1991).
[7] L. Hatvani, On the asymptotic stability for nonautonomous functional differential equations by Liapunov functionals, Trans. Amer. Math. Soc. 354 (2002) 3555–3571.

Citation :

Sanjay K. Srivastava, Neha Wadhwa, Neeti Bhandari, "Stability of Impulsive Functional Differential Equations via Lyapunov Functionals," International Journal of Mathematics Trends and Technology (IJMTT), vol. 30, no. 2, pp. 100-103, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V30P518

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