中文摘要：

针对线性离散时滞系统的时滞相关稳定性问题进行研究,提出一个新的有限和不等式,是Abel型不等式的进一步推广.利用这一不等式和构造适当的Lyapunov-Krasovskii泛函,给出新的离散时滞系统稳定性判别准则,并应用数值例子进行验证.验证结果表明,所提出方法与Abel型不等式方法相比,能够获得更大的允许上界,比用自由权方法使用更少的决策变量,降低了数值计算负担,进一步表明了所得结果的有效性和优越性.

英文摘要：

This paper is concerned with stability of linear discrete time-delay systems. Firstly, a new finite-sum inequality is proposed, which is the further promotion for Abel lemma-based finite-sum inequality. Then, by using the inequality and constructing appropriate Lyapunov-Krasovskii functionals（LKFs）, a new delay-dependent stability criteria is obtained in terms of linear matrix inequalities（LMIs）. Numerical examples are given to demonstrate that the proposed method can provide a larger admissible maximum upper bound than those using the Abel lemma-based finite-sum inequality approach, and it involves less decision variables than the free-weighting matrix method.