This article deals with the problem of delay-dependent finite-time stability (FTS) for delayed discrete-time systems with nonlinear perturbations. First, based on a Lyapunov–Krasovskii Functional, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, a new reduced free-matrix-based inequality is established to estimate the single summation term. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore our method is more effective. Thus, less conservative design conditions are obtained in this paper in terms of linear matrix inequalities (LMIs) and solved using MATLAB’s LMI toolbox to achieve the desired performance. The purpose of this paper is to derive sufficient conditions that ensure the finite-time stability of the discrete-time system. Finally, numerical examples are examined to show the advantage and effectiveness of the proposed results.

本文讨论具有非线性扰动的延迟离散时间系统的延迟相关有限时间稳定性 (FTS) 问题。首先，基于Lyapunov-Krasovskii泛函，通过引入一些自由权矩阵来提供依赖于延迟的FTS条件。然后，建立一个新的基于简化自由矩阵的不等式来估计单个求和项。我们的结果中这些自由矩阵积分的维数小于文献中获得的维数。变量数量的减少并不意味着我们的方法是特殊情况，而只是意味着我们的方法与其他方法完全不同，因此我们的方法更有效。因此，本文在线性矩阵不等式 (LMI) 方面获得了不太保守的设计条件，并使用 MATLAB 的 LMI 工具箱进行求解，以实现所需的性能。本文的目的是推导确保离散时间系统有限时间稳定性的充分条件。最后，通过数值算例验证了所提出结果的优点和有效性。