The stability and stabilization of a class of nonlinear discrete time delayed systems(NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov–Krasovskii functional method, a sufficient delaydependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller(DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality(LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to uncertain discrete time delayed systems(UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties. The stability and stabilization of a class of nonlinear discrete time delayed systems (NDTDS) with time-varying delay and norm-bounded nonlinearity are investigated. Based on discrete time Lyapunov-Krasovskii functional method, a sufficient delay dependent condition for asymptotic stability of nonlinear systems is offered. Then, this condition is used to design a new efficient delayed state feedback controller (DSFC) for stabilization of such systems. These conditions are in the linear matrix inequality (LMI) framework. Illustrative examples confirm the improvement of the proposed approach over the Similar cases. Furthermore, the obtained stability and stabilization conditions will be extended to unstable discrete time delayed systems (UDTDS) with polytopic parameter uncertainties and also with norm-bounded parameter uncertainties.