Asymptotic behaviors of non-autonomous impulsive difference equation with delays

In this paper, some new methods are established to research the asymptotic behaviors of non-autonomous impulsive difference equations with delays. According to properties of nonnegative matrices and nonsingular MM-matrices, we derive several sufficient criteria on global exponential stability, global attracting set and ultimately bounded by constructing an improved time-varying difference inequality. Some numerical examples are given to demonstrate the efficiency of proposed methods.