Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties

Yujuan Tian,Yuhan Yin,Kening Wang,Fei Wang

doi:10.3390/math10030526

Yujuan Tian, Yuhan Yin + Show 2 more

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https://doi.org/10.3390/math10030526

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Abstract

This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs into real and imaginary parts, some stability criteria in terms of complex-valued linear matrix inequalities (LMIs) are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed. Moreover, a new impulsive differential inequality is applied to resolve the difficulties caused by the mixed time delays and delayed impulse effects. Finally, an illustrative example is provided to back up our theoretical results.

Highlights

In recent decades, neural network models have a lot of potential to be used in various fields such as pattern classification, optoelectronics, associative memory and signal processing [1,2,3,4,5]
Our results extend those of previous studies [37,40]; and (iii) a new impulsive differential inequality is employed to resolve the difficulties caused by the delayed impulse effects and mixed delays
Some stability criteria are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed or not; (iii) in [40], the stability of impulsive complexvalued neural networks (CVNNs) with constant delays was studied by utilizing the complex-valued Lyapunov–Razumikhin technique, where the stability criterion is obtained by analytical inequalities of matrix eigenvalues

Summary

Introduction

Neural network models have a lot of potential to be used in various fields such as pattern classification, optoelectronics, associative memory and signal processing [1,2,3,4,5]. The major contributions can be listed as follows: (i) a comprehensive model of CVNNs which simultaneously contains uncertain parameters and mixed time-delays is discussed; (ii) by constructing complex-valued Lyapunov function and designing a delayed impulsive controller, some stability criteria are derived for CVNNs, which are valid regardless of whether the activation functions can be decomposed. Our results extend those of previous studies [37,40]; and (iii) a new impulsive differential inequality is employed to resolve the difficulties caused by the delayed impulse effects and mixed delays.

Main Results

Numerical Examples

Conclusions