New summation inequalities and their applications to discrete-time delay systems

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.Comment: 15 pages, 01 figur

STABILITY, FINITE-TIME STABILITY AND PASSIVITY CRITERIA FOR DISCRETE-TIME DELAYED NEURAL NETWORKS

In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology

Finite-Time Stability for Discrete-Time Systems with Time-Varying Delays and Nonlinear Perturbations Using Relaxed Summation Inequality

Producción CientíficaThis 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.MICInn, PID2021-123654OB-C31MICInn, PID2020-112871RB-C2