$ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay

Jingya Wang; Ye Zhu; Jingya Wang; Ye Zhu

doi:10.3934/mbe.2023588

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 13182-13199. doi: 10.3934/mbe.2023588

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Research article

$ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay

Jingya Wang ^,,
Ye Zhu

School of Computer Science and Technology, Anhui University of Technology, Ma'anshan 243032, China

Academic Editor: Yang Kuang

Received: 28 April 2023 Revised: 26 May 2023 Accepted: 31 May 2023 Published: 08 June 2023

This paper investigates $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive neural networks (MNNs) with a non-necessarily differentiable time-varying delay. The objective is to design an output-feedback controller to ensure the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability of the considered MNN. A criterion on the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability is proposed using a Lyapunov functional, the Bessel-Legendre inequality, and the convex combination inequality. Then, a linear matrix inequalities-based design scheme for the required output-feedback controller is developed by decoupling nonlinear terms. Finally, two examples are presented to verify the proposed $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability criterion and design method.
- memristive neural network (MNNs),
- $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control,
- asymptotic stability,
- time-varying delay
Citation: Jingya Wang, Ye Zhu. $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive NNs with non-necessarily differentiable time-varying delay[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 13182-13199. doi: 10.3934/mbe.2023588

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Abstract

This paper investigates $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ control for memristive neural networks (MNNs) with a non-necessarily differentiable time-varying delay. The objective is to design an output-feedback controller to ensure the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability of the considered MNN. A criterion on the $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability is proposed using a Lyapunov functional, the Bessel-Legendre inequality, and the convex combination inequality. Then, a linear matrix inequalities-based design scheme for the required output-feedback controller is developed by decoupling nonlinear terms. Finally, two examples are presented to verify the proposed $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ stability criterion and design method.

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