Improved Extended Dissipativity Results for T-S Fuzzy Generalized Neural Networks With Mixed Interval Time-Varying Delays

Sunisa Luemsai,Thongchai Botmart

doi:10.1109/access.2021.3139633

Sunisa Luemsai, Thongchai Botmart

Open Access

https://doi.org/10.1109/access.2021.3139633

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Journal: IEEE Access	Publication Date: Jan 1, 2022
Citations: 5	License type: CC BY 4.0

Affiliation: Khon Kaen University

Abstract

The asymptotic stability and extended dissipativity performance of T-S fuzzy generalized neural networks (GNNs) with mixed interval time-varying delays are investigated in this paper. It is noted that this is the first time that extended dissipativity performance in the T-S fuzzy GNNs has been studied. To obtain the improved results, we construct the Lyapunov-Krasovskii functional (LKF), which consists of single, double, triple, and quadruple integral terms containing full information of the delays and a state variable. Moreover, an improved Wirtinger inequality, a new triple integral inequality, and zero equation, along with a convex combination approach, are used to deal with the derivative of the LKF. By using Matlab’s LMI toolbox and the above methods, the new asymptotic stability and extended dissipativity conditions are gained in the form of linear matrix inequalities (LMIs), which include passivity, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}-L_{\infty }$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> , and dissipativity performance. Finally, numerical examples that are less conservative than previous results are presented. Furthermore, we give numerical examples to demonstrate the correctness and efficacy of the proposed method for asymptotic stability and extended dissipativity performance of the T-S fuzzy GNNs, including a particular case of the T-S fuzzy GNNs.

Highlights

V ARIOUS types of neural networks (NNs) have attracted the attention of researchers in the past few decades because neural networks have a wide range of applications in many fields such as combinatorial optimization, speed detection of moving objects, pattern classification, associative memory design, and other areas [1]–[5]
Time delays cannot be avoided in the analysis of stability and performance for NNs, and many researchers have studied NNs with distributed and discrete time delays [9]–[11]
In this article, we investigated the extended dissipativity problem for the T-S fuzzy generalized neural networks (GNNs) with mixed interval timevarying delays

Summary

Introduction

V ARIOUS types of neural networks (NNs) have attracted the attention of researchers in the past few decades because neural networks have a wide range of applications in many fields such as combinatorial optimization, speed detection of moving objects, pattern classification, associative memory design, and other areas [1]–[5]. An essential factor affecting the model of the system to be used in the stability analysis is the time delay. Since the variety of sizes and lengths of the axon, nerve impulses are distributed, which causes the distributed time delay [8]. The presence of such delays frequently leads to system instability, oscillation, and decreased performance. Time delays cannot be avoided in the analysis of stability and performance for NNs, and many researchers have studied NNs with distributed and discrete time delays [9]–[11]. Mixed interval time-varying delays can occur in many actual industrial systems, such as the reduced-order aggregate model for large-scale converters [12], a multiagent-based consensus algorithm in the energy internet [13], dual-predictive control for AC microgrids [14]

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