Stability of linear neutral differential equations with delays and impulses established by the fixed points method

In this paper, we consider the impulsive effects on the stability of the zero solution of the linear neutral differential equations with variable delays. By transforming the equations into ones without impulses and using fixed point theory, some sufficient conditions for asymptotic stability and exponential stability of the zero solution are obtained. The paper extends and improves results on sufficient conditions obtained by Jin and Luo (2008) [17], and Ardjouni and Djoudi (2011) [18], which is shown clearly in Example 1. This paper also shows that the impulse intensity and the impulse time both influence the decay rate of the convergence to zero of the solutions. Finally, two examples are given to show applications of some results obtained.