Improved Results onH∞State Estimation of Static Neural Networks with Time Delay

Bin Wen,Shouming Zhong,Hui Li

doi:10.1155/2016/1759650

Abstract

This paper studies the problem ofH∞state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribedH∞performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.

Highlights

Neural networks (NNs) have drawn a great deal of attention due to their extensive applications in various fields such as associative memory, pattern recognition, signal processing, combinatorial optimization, and adaptive control [1,2,3]
We mainly focus on static neural networks (SNNs) in this paper, which is one type of recurrent neural networks (RNNs)
The main difference between SNNs and local field neural networks is whether the neuron states or the local field states of neurons are taken as basic variables

Summary

Introduction

Neural networks (NNs) have drawn a great deal of attention due to their extensive applications in various fields such as associative memory, pattern recognition, signal processing, combinatorial optimization, and adaptive control [1,2,3]. Among them H∞ state estimation of static neural networks with time delay was studied in [17,18,19, 28, 30, 31]. In [28], a delay partition approach was proposed to deal with the state estimation problem for a class of static neural networks with time-varying delay. In [30], the state estimation problem of the guaranteed H∞ and H2 performance of static neural networks was considered. The exponential state estimation of time-varying delayed neural networks was studied in [19]. This paper investigates the problem of H∞ state estimation for a class of delayed static neural networks. If their dimensions are not explicitly stated, are assumed to be compatible for algebraic operations

Problem Formulation

State Estimator Design

Numerical Examples

Conclusions