Extreme stability in terms of two measures for difference systems with finite delay

In this paper, we first introduce the conception of extreme stability in terms of two measures for difference systems with finite delay, then we establish some theorems which can ascertain the (h₀,h) extreme-stability (extreme-uniform stability, extreme-asymptotic stability, extreme-uniform asymptotic stability) of delay difference systems. In the obtained theorems, ΔV is not required to be always negative, especially, ΔV may be even positive, which are more convenient to use. At the end, we give an example to show the application of the obtained results.