Design disturbance attenuating controller for memristive recurrent neural networks with mixed time-varying delays

Jianying Xiao,Fang Xu,Shouming Zhong

doi:10.1186/s13662-018-1641-8

Abstract

This paper investigates the design of disturbance attenuating controller for memristive recurrent neural networks (MRNNs) with mixed time-varying delays. By applying the combination of differential inclusions, set-valued maps and Lyapunov–Razumikhin, a feedback control law is obtained in the simple form of linear matrix inequality (LMI) to ensure disturbance attenuation of memristor-based neural networks. Finally, a numerical example is given to show the effectiveness of the proposed criteria.

Highlights

It is well known that the neural networks are so important that they have been widely applied in various areas such as reconstructing moving images, signal processing, pattern recognition, optimization problems and so on
Let us recall the brief development of memristive neural networks in the following
With the rapid development of science, a prototype of the memristor had been built by some scientists from HP Labs until 2008

Summary

Introduction

It is well known that the neural networks are so important that they have been widely applied in various areas such as reconstructing moving images, signal processing, pattern recognition, optimization problems and so on (for reference, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]). Theorem 3.1 Under Assumption 2.1, the memristive neural network (7) with h(t) = 0 under a disturbance attenuating controller u(t) = –Fx(t) is asymptotically stable if there exist matrices Q > 0, F, positive constants εi (i = 0, 1, 2), and any given positive constant such that the following inequality holds:. Theorem 3.2 Under Assumption 2.1, the memristive neural network (7) with h(t) = 0 has a disturbance attenuating controller u(t) = –Fx(t) with an attractor as = {x|xT Qx ≤ 1} if there exist matrices Q > 0, M, F, positive constants εi (i = 0, 1, 2), and any given positive constant such that the following inequality holds:

11 QG QB QC ρQD

Conclusions