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.
