Impulsive stabilization of functional differential equations with infinite delays

Abstract In this paper, we study the stability of a class of impulsive functional differential equations with infinite delays. We establish a uniform stability theorem and a uniform asymptotic stability theorem, which shows that certain impulsive perturbations may make unstable systems uniformly stable, even uniformly asymptotically stable.

[1]  Xinzhi Liu.  Impulsive stabilization of nonlinear systems , 1993 .

[2]  G. Seifert.  Liapunov-Razumikhin conditions for asymptotic stability in functional differential equations of Volterra type , 1974 .

[3]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[4]  Zhiguo Luo,et al.  Stability and boundedness for impulsive functional differential equations with infinite delays , 2001 .

[5]  Jianhua Shen,et al.  Razumikhin type stability theorems for impulsive functional differential equations 1 1 Research was , 1998 .

[6]  V. Kolmanovskii,et al.  Stability of Functional Differential Equations , 1986 .

[7]  J. R. Haddock.  Friendly Spaces for Functional Differential Equations with Infinite Delay , 1985 .

[8]  R. Grimmer,et al.  Stability properties of Volterra integrodifferential equations , 1975 .

[9]  S. Sivasundaram,et al.  Stability of Volterra integro-differential equations with impulsive effect , 1992 .

[10]  V. Lakshmikantham,et al.  Theory of Differential Equations with Unbounded Delay , 1994 .

[11]  Jianhua Shen,et al.  Stability results for impulsive functional differential equations with infinite delays , 2001 .

[12]  Jianhua Shen,et al.  Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions , 1999 .

[13]  Xinzhi Liu,et al.  Uniform asymptotic stability of impulsive delay differential equations , 2001 .

[14]  J. Ridenhour.  On the zeros of solutions of Nth order linear differential equations , 1974 .

[15]  J. Hale.  Theory of Functional Differential Equations , 1977 .