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Impulsive integro-differential systems which are an important embranchment of nonlinear impulsive differential systems, arise from extensive applications in nature-science such as mathematic models of circuit simulation in physics and neuronal networks in biology. Consequently there are some results about stability of such systems by vector Lyapunov functions coupled with Razumikhin techniques. However, it's difficult to choose a right vector Lyapunov function because of the restrict conditions. At the same time, the method of cone-valued Lyapunov functions is well known to be advantageous in applications. Hence, the stability results for impulsive integro-differential systems could be improved via the method of cone-valued Lyapunov functions.
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