Improved results on mixed passive and $ H_{\infty} $ performance for uncertain neural networks with mixed interval time-varying delays via feedback control

Sunisa Luemsai; Thongchai Botmart; Wajaree Weera; Suphachai Charoensin; Sunisa Luemsai; Thongchai Botmart; Wajaree Weera; Suphachai Charoensin

doi:10.3934/math.2021161

AIMS Mathematics

2021, Volume 6, Issue 3: 2653-2679. doi: 10.3934/math.2021161

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Research article

Improved results on mixed passive and $ H_{\infty} $ performance for uncertain neural networks with mixed interval time-varying delays via feedback control

1.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
2.
Department of Mathematics, Faculty of Science, University of PhaYao, PhaYao, 56000, Thailand
3.
Department of Nutrition School of Medical Sciences, University of PhaYao, PhaYao, 56000, Thailand

Received: 30 October 2020 Accepted: 24 December 2020 Published: 31 December 2020
MSC : 34D20, 34H15

This paper studies the mixed passive and $ H_{\infty} $ performance for uncertain neural networks with interval discrete and distributed time-varying delays via feedback control. The interval discrete and distributed time-varying delay functions are not assumed to be differentiable. The improved criteria of exponential stability with a mixed passive and $ H_{\infty} $ performance are obtained for the uncertain neural networks by constructing a Lyapunov-Krasovskii functional (LKF) comprising single, double, triple, and quadruple integral terms and using a feedback controller. Furthermore, integral inequalities and convex combination technique are applied to achieve the less conservative results for a special case of neural networks. By using the Matlab LMI toolbox, the derived new exponential stability with a mixed passive and $ H_{\infty} $ performance criteria is performed in terms of linear matrix inequalities (LMIs) that cover $ H_{\infty} $, and passive performance by setting parameters in the general performance index. Numerical examples are shown to demonstrate the benefits and effectiveness of the derived theoretical results. The method given in this paper is less conservative and more general than the others.
- uncertain neural networks,
- mixed passive and $ H_{\infty} $ performance,
- exponential stability,
- mixed interval time-varying delays,
- feedback control
Citation: Sunisa Luemsai, Thongchai Botmart, Wajaree Weera, Suphachai Charoensin. Improved results on mixed passive and $ H_{\infty} $ performance for uncertain neural networks with mixed interval time-varying delays via feedback control[J]. AIMS Mathematics, 2021, 6(3): 2653-2679. doi: 10.3934/math.2021161

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Abstract

This paper studies the mixed passive and $ H_{\infty} $ performance for uncertain neural networks with interval discrete and distributed time-varying delays via feedback control. The interval discrete and distributed time-varying delay functions are not assumed to be differentiable. The improved criteria of exponential stability with a mixed passive and $ H_{\infty} $ performance are obtained for the uncertain neural networks by constructing a Lyapunov-Krasovskii functional (LKF) comprising single, double, triple, and quadruple integral terms and using a feedback controller. Furthermore, integral inequalities and convex combination technique are applied to achieve the less conservative results for a special case of neural networks. By using the Matlab LMI toolbox, the derived new exponential stability with a mixed passive and $ H_{\infty} $ performance criteria is performed in terms of linear matrix inequalities (LMIs) that cover $ H_{\infty} $, and passive performance by setting parameters in the general performance index. Numerical examples are shown to demonstrate the benefits and effectiveness of the derived theoretical results. The method given in this paper is less conservative and more general than the others.

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