Hybrid Feedback Control for Exponential Stability and Robust H∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

Chantawat, Charuwat; Botmart, Thongchai; Supama, Rattaporn; Weera, Wajaree; Noinang, Sakda

doi:10.3390/computation9060062

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Hybrid Feedback Control for Exponential Stability and Robust H_∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

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Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Department of Mathematics, Faculty of Science, University of Phayao, Phayao 56000, Thailand

Department of Mathematics Statistics and Computer, Faculty of Science, Ubon Ratchathani University, Ubon Ratchathani 34190, Thailand

Authors to whom correspondence should be addressed.

Academic Editors: Yongwimon Lenbury, Ravi P. Agarwal, Philip Broadbridge and Dongwoo Sheen

Computation 2021, 9(6), 62; https://doi.org/10.3390/computation9060062

Received: 29 April 2021 / Revised: 19 May 2021 / Accepted: 25 May 2021 / Published: 28 May 2021

(This article belongs to the Special Issue Proceedings of the International Conference in Mathematics and Applications 2020_Mahidol University)

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Abstract

This paper is concerned the problem of robust

H_{\infty}

control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with

H_{\infty}

performance attenuation level

γ

. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust

H_{\infty}

control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods. View Full-Text

Keywords: neural networks; H_∞ control; hybrid feedback control; mixed time-varying delay

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Chantawat, C.; Botmart, T.; Supama, R.; Weera, W.; Noinang, S. Hybrid Feedback Control for Exponential Stability and Robust H_∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays. Computation 2021, 9, 62. https://doi.org/10.3390/computation9060062

AMA Style

Chantawat C, Botmart T, Supama R, Weera W, Noinang S. Hybrid Feedback Control for Exponential Stability and Robust H_∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays. Computation. 2021; 9(6):62. https://doi.org/10.3390/computation9060062

Chicago/Turabian Style

Chantawat, Charuwat, Thongchai Botmart, Rattaporn Supama, Wajaree Weera, and Sakda Noinang. 2021. "Hybrid Feedback Control for Exponential Stability and Robust H_∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays" Computation 9, no. 6: 62. https://doi.org/10.3390/computation9060062

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Hybrid Feedback Control for Exponential Stability and Robust H_∞ Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays

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