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Non-fragile robust finite-time stabilization and \(H_{\infty }\) performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching

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Abstract

In this paper, the global non-fragile robust finite-time stabilization and \(H_{\infty }\) performance analysis are investigated for uncertain switched fractional-order neural networks with discontinuous activations, time delay and external disturbance under the asynchronous switching. Firstly, a new inequality, which is concerned with the fractional derivative of the variable upper limit integral for the nonsmooth integrable functional, is developed. Secondly, the non-fragile switched controller with two types of gain perturbations is designed. Under the Filippov fractional differential inclusion framework, the global non-fragile robust finite-time stabilization conditions are addressed in terms of linear matrix inequalities (LMIs) by applying nonsmooth analysis theory, inequality analysis technique, average dwell-time method and Lyapunov functional approach. In addition, the global non-fragile robust finite-time \(H_{\infty }\) performance analysis is performed, and the global non-fragile robust finite-time stabilization conditions with \(H_{\infty }\) disturbance attenuation level are also derived in the form of LMIs. Finally, two numerical examples are given to illustrate the feasibility of the proposed non-fragile switched controller and the validity of the theoretical results.

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Abbreviations

R :

Real numbers set

C :

Complex numbers set

\(N_{+}\) :

Positive integers set

\(R^{n}\) :

n-dimensional Euclidean space

\(R^{m \times n}\) :

\(m \times n\) real matrices set

\(*\) :

Symmetric term

diag \(\{\cdot \}\) :

Block-diagonal matrix

\(A^{T}\) :

Transpose of A

\(A>0\) :

Positive definite matrix A

\(A<0\) :

Negative definite matrix A

\(\lambda _{\max }(A)\) :

Maximum eigenvalue of the symmetric matrix A

\(\lambda _{\min }(A)\) :

Minimum eigenvalue of the symmetric matrix A

\(I_{n}\) :

n-dimensional identity matrix

\(L_{2}\) :

The space of square-summable n-dimensional vector function

\(c([-\tau, 0]; R^{n})\) :

The family of continuous function \(\phi\) from \([-\tau, 0]\) to \(R^{n}\)

\( \bar{c}o[\varOmega ] \) :

Closure of the convex hull of Ω

NNs:

Neural networks

FNNs:

Fractional-order neural networks

SNNs:

Switched neural networks

SFNNs:

Switched fractional-order neural networks

USFNNs:

Uncertain switched fractional-order neural networks

FTB:

Finite-time bounded

ADT:

Average dwell time

LMIs:

Linear matrix inequalities

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Acknowledgements

The authors would like to thank the Editors and the Reviewers for their insightful and constructive comments, which help to enrich the content and improve the presentation of the results in this paper.

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  1. School of Science, Yanshan University, Qinhuangdao, 066001, China

    Xiao Peng & Huaiqin Wu

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  1. Xiao Peng
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Peng, X., Wu, H. Non-fragile robust finite-time stabilization and \(H_{\infty }\) performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching. Neural Comput & Applic 32, 4045–4071 (2020). https://doi.org/10.1007/s00521-018-3682-z

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