The stability problem of discrete-time linear systems with interval time-varying delays is investigated in this paper. According to the latest summation inequality technique, an improved free-matrix-based summation inequality is proposed in this paper. In order to make full use of the improved inequality to bound the upper bounds of the difference Lyapunov-Krasovskii functional (LKF), an augmented LKF with some extra status information is constructed. A new delay-range-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs) via the modified LKF approach. The criterion is less conservative than some existing results. Finally, some standard numerical examples are presented the effectiveness of the proposed approach.

本文研究了具有区间时变时滞的离散时间线性系统的稳定性问题。根据最新的求和不等式技术，本文提出了一种改进的基于自由矩阵的求和不等式。为了充分利用改进的不等式来限制Lyapunov-Krasovskii泛函（LKF）的上界，构造了一个带有一些额外状态信息的增广LKF。通过改进的 LKF 方法，以线性矩阵不等式 (LMI) 的形式导出了一种新的与延迟范围相关的稳定性准则。该标准不如一些现有结果保守。最后，一些标准的数值例子展示了所提出方法的有效性。