Robust passivity analysis of mixed delayed neural networks with interval nondifferentiable time-varying delay based on multiple integral approach

Thongchai Botmart; Sorphorn Noun; Kanit Mukdasai; Wajaree Weera; Narongsak Yotha; Thongchai Botmart; Sorphorn Noun; Kanit Mukdasai; Wajaree Weera; Narongsak Yotha

doi:10.3934/math.2021170

AIMS Mathematics

2021, Volume 6, Issue 3: 2778-2795. doi: 10.3934/math.2021170

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Research article

Robust passivity analysis of mixed delayed neural networks with interval nondifferentiable time-varying delay based on multiple integral approach

1.
Department of Mathematics, Khon Kaen University, Khon Kaen 40002, Thailand
2.
Department of Mathematics, University of Pha Yao, Pha Yao 56000, Thailand
3.
Department of Applied Mathematics and Statistics, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, Thailand

Received: 25 October 2020 Accepted: 22 December 2020 Published: 06 January 2021
MSC : 34K25, 93D05, 93D09

New results on robust passivity analysis of neural networks with interval nondifferentiable and distributed time-varying delays are investigated. It is assumed that the parameter uncertainties are norm-bounded. By construction an appropriate Lyapunov-Krasovskii containing single, double, triple and quadruple integrals, which fully utilize information of the neuron activation function and use refined Jensen's inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.
- passivity analysis,
- neural networks,
- uncertainties,
- nondifferentiable delay,
- time-varying delays
Citation: Thongchai Botmart, Sorphorn Noun, Kanit Mukdasai, Wajaree Weera, Narongsak Yotha. Robust passivity analysis of mixed delayed neural networks with interval nondifferentiable time-varying delay based on multiple integral approach[J]. AIMS Mathematics, 2021, 6(3): 2778-2795. doi: 10.3934/math.2021170

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Abstract

New results on robust passivity analysis of neural networks with interval nondifferentiable and distributed time-varying delays are investigated. It is assumed that the parameter uncertainties are norm-bounded. By construction an appropriate Lyapunov-Krasovskii containing single, double, triple and quadruple integrals, which fully utilize information of the neuron activation function and use refined Jensen's inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Three numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.

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