Asymptotic Stability of Delay-Difference Equations via Matrix Inequalities and Applications

In this paper, by using a discrete version of the second Lyapunov method, we derive a suf- ficient condition independent of the delay for the asymptotic stability of delay-difference equations. The result is applied to obtain new stability conditions in terms of matrix inequalities for some classes of delay-difference equations such as high-order equations, perturbed equations, control systems and switched delay systems. Our results can be considered as further developments of existing results on stability theory of delay-difference systems and applications.