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

Chalida Phanlert,Thongchai Botmart,Prem Junsawang,Wajaree Weera

doi:10.1109/access.2021.3089374

Abstract

In this article, we consider the finite-time mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> /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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> , passivity, and finite-time 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.

Highlights

F OR a number of years, neural networks have been widely attended in many fields, for instance, model identification, optimization, parallel computation, associative memories design, image processing, and other engineering fields [1]–[28]
FINITE-TIME BOUNDEDNESS In this subsection, we study finite-time boundedness for the generalized neural networks in the following form: z(t) = −Az(t) + B0f (W z(t)) + B1g(W z(t − ι(t)))
It is noticed that our results presented larger bounds of time-delay than the existing literature by using the multiple integral terms Lyapunov-Krasovskii function combined with inequalities

Summary

Introduction

F OR a number of years, neural networks have been widely attended in many fields, for instance, model identification, optimization, parallel computation, associative memories design, image processing, and other engineering fields [1]–[28]. We consider the finite-time mixed H∞/passivity, finitetime stability, and finite-time boundedness for the generalized neural networks problems with both interval distributed and discrete time-varying delays.

Results

Conclusion