A New Technique in Stability of Infinite Delay Differential Equations With Impulsive Effects
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Keywords:
Impulsive infinite delay differential equations, Uniform stability, Lyapunov functions, Razumikhin techniqueAbstract
In this work, we consider the stability of impulsive infinite delay differential equations. A new technique is derived to establish the stability criteria for impulsive infinite delay differential equations. By using Lyapunov functions and Razumikhin technique, some results are obtained which are more general than ones existing in literature. Lyapunov functionals are adopted and components of x are divided into several groups, correspondingly, several functions $V_j\left(t,x^{\left(j\right)}\right)$, ($j=1,2,\dots,m$) are employed. It is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behaviour. An example is also presented to illustrate the efficiency of the result obtained.
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