Finite-Time MixedH_∞/Passivity for Neural Networks With Mixed Interval Time-Varying Delays Using the Multiple Integral Lyapunov-Krasovskii Functional

Abstract

In this article, we consider the finite-time mixed H ∞ /passivity, finite-time stability, and finite-time boundedness for generalized neural networks with interval distributed and discrete time-varying delays. It is noted that this is the first time for studying in the combination of H ∞ , passivity, and finitetime boundedness. To obtain several sufficient criteria achieved in the form of linear matrix inequalities (LMIs), we introduce an appropriate Lyapunov-Krasovskii function (LKF) including single, double, triple, and quadruple integral terms, and estimating the bound of time derivative in LKF with the use of Jensen's integral inequality, an extended single and double Wirtinger's integral inequality, and a new triple integral inequality. These LMIs can be solved by using MATLAB's LMI toolbox. Finally, five numerical simulations are shown to illustrate the effectiveness of the obtained results. The received criteria and published literature are compared.INDEX TERMS neural networks, Lyapunov-Krasovskii function, H ∞ and passivity, time-varying delays, finite-time bounded

Robust Mixed Performance Control of Uncertain T-S Fuzzy Systems With Interval Time-Varying Delay by Sampled-Data Input

“…In the past, the H ∞ performance of systems under consideration was used to minimize the effect of regulated output with respect to disturbance input and guarantee that the closed-loop system is stable [4], [7], [9], [12], [20], [21], [25]- [27]. On the other hand, the H 2 performance of systems was applied to minimize the dynamics with respect to initial condition of system under consideration and zero disturbance.…”

Finite-Time Passivity Analysis of Neutral-Type Neural Networks with Mixed Time-Varying Delays

“…This topic has piqued the curiosity of researchers [28][29][30][31][32][33][34][35]. They deal with by Jensen's and Coppel's inequality in [28], which is concerned with the problem of finite-time stability of continuous time delay systems.…”

“…Ali et al [34] explored popular topics including the finite-time H ∞ boundedness of discrete-time neural networks and norm-bounded disturbances with time-varying delay. In 2021, Phanlert et al [35] has been researching a finite-time nonneutral system. Based on the above research, there are many different methods for stability analysis.…”

“…5, 0.9}. Using the MATHLAB tools to solve LMIs(35) and (36), we may obtain γ = 17.4493, indicating that the neutral system under consideration is finite-Consider the following matrix parameters for the neutral-type neural networks:…”

“…4, 0.8}. Using the MATHLAB tools to solve LMIs(35) and(36), we indicate that the neutral system under consideration is finite-time passive. In addition, the acquired results are compared to previously published studies.…”