Abstract
In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system's parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique.