The systems with interval time-delay appearing in state variable have wide application

and can be used to describe a class of networked control systems. The stability analysis and the state feedback controller design are investigated for linear discrete-time systems with interval time delays. In order to investigate the stability

a new Lyapunov-Krasovskii functional is proposed by introducing the double summation and triple summation. In order to estimate the difference of the Lyapunov-Krasovskii functional

the Abel lemma based finite sum inequality technique and the time delay segmentation method are used as tools

and thus a sufficient condition is presented for the asymptotic stability of the considered systems in terms of linear matrix inequalities. Compared to the traditional Lyapunov functional

since the proposed Lyapunov-Krasovskii functional contains more information on delays

and the approach for estimating the difference does not involve model transformation

thus the presented sufficient condition for the asymptotic stability of the system is less conservative. In addition

compared with the previous free-weighting matrix method there exist less feasible matrix variables in the current method. Thus

the computational load can be effectively reduced. According to the derived stability criterion

a design approach for non-memory state feedback controllers is presented in terms of linear matrix inequalities

and thus has good numerical stability. Finally a numerical example is employed to illustrate the effectiveness of the methods proposed in this paper.