UNIFORM EXPONENTIAL STABILITY OF IMPULSIVE DELAY DIFFERENTIAL SYSTEMS

Bhanu Gupta (India), Sanjay K. Srivastava (India) and Aakanksha Mahajan (India)

Received July 26, 2009

References:

[1] A. Anokhin, L. Berezansky and E. Braverman, Exponential stability of linear delay impulsive differential equations, J. Math. Anal. Appl. 193(3) (1995), 923-941. [2] G. Ballinger and X. Lui, Existence, uniqueness and boundedness results for impulsive delay differential equations, Appl. Anal. 74(1-2) (2000), 71-93. [3] L. Berezansky and L. Idels, Exponential stability of some scalar impulsive delay differential equations, Commun. Appl. Math. Anal. 2(3) (1998), 301-309. [4] J. Hale, Theory of Functional Differential Equations, Springer, New York, 1977. [5] V. Lakshmikantham, D. D. Baĭnov and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. [6] N. M. Linh and V. N. Phat, Exponential stability of nonlinear time-varying differential equations and applications, Electron. J. Differential Equations 34 (2001), 1-13. [7] Z. Luo and J. Shen, New Razumikhin type theorems for impulsive functional differential equations, Appl. Math. Comput. 125(2-3) (2002), 375-386. [8] Q. Wang and X. Liu, Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method, Appl. Math. Lett. 20(8) (2007), 839-845. [9] Y. Zang and J. Sun, Eventual stability of impulsive differential systems, Acta Math. Sci. Ser. B 27(2) (2007), 373-380. [10] Y. Zang and J. Sun, Stability of impulsive functional differential equations, Nonlinear Anal. 68(12) (2008), 3665-3678.

Keywords and phrases: impulsive delay differential system, Lyapunov function, exponential stability, Razumikhin technique.