Further analysis on uniform stability of impulsive infinite delay differential equations

Abstract A criterion for the uniform stability of impulsive functional differential equations with infinite delays is presented by using Lyapunov functions and the Razumikhin technique. The criterion is more general than several recent works. An example showing the effectiveness and advantage of the present criterion is given.

[1]  Xilin Fu,et al.  Razumikhin-type theorems on exponential stability of impulsive infinite delay differential systems , 2009 .

[2]  Alexander O. Ignatyev,et al.  On the stability of invariant sets of systems with impulse effect , 2008 .

[3]  Ivanka M. Stamova,et al.  Lyapunov—Razumikhin method for impulsive functional differential equations and applications to the population dynamics , 2001 .

[4]  Jianhua Shen.  Razumikhin techniques in impulsive functional differential equations , 1999 .

[5]  Yu Zhang,et al.  Stability of impulsive infinite delay differential equations , 2006, Appl. Math. Lett..

[6]  Xiaodi Li.  Uniform asymptotic stability and global stability of impulsive infinite delay differential equations , 2009 .

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

[8]  Xiaodi Li,et al.  New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays , 2010 .

[9]  K. Gopalsamy,et al.  On delay differential equations with impulses , 1989 .

[10]  Xinzhi Liu,et al.  On stability in terms of two measures for impulsive systems of functional differential equations , 2007 .

[11]  Zhiguo Luo,et al.  New Razumikhin type theorems for impulsive functional differential equations , 2002, Appl. Math. Comput..

[12]  Yu Zhang,et al.  Stability of impulsive functional differential equations , 2008 .

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