Difference inequality for stability of impulsive difference equations with distributed delays

In this paper, we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the properties of "ρ-cone" and eigenspace of the spectral radius of non-negative matrices, some new sufficient conditions for global exponential stability of the impulsive difference equations with distributed delays are obtained. An example is given to demonstrate the effectiveness of the theory.