New results on H_{infty} state estimation of static neural networks with time-varying delay

Bin Wen,Hui Li,Shouming Zhong

doi:10.1186/s13662-016-1056-3

Abstract

This paper is concerned with the problem of H_{infty} state estimation problem 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 with a prescribed H_{infty} performance. Some improved delay-dependent conditions are established by using delay partitioning method and the free-matrix-based integral inequality. The gain matrix and the optimal performance index are obtained via solving a convex optimization problem subject to LMIs (linear matrix inequality). Numerical examples are provided to illustrate the effectiveness of the proposed method comparing with some existing results.

Highlights

Neural networks (NNs) have attracted a great deal of attention because of their extensive applications in various fields such as associative memory, pattern recognition, combinatorial optimization, adaptive control, etc. [, ]
We mainly focus on static neural networks (SNNs) in this paper, which is one type of recurrent neural networks
According to whether the neuron states or the local field states of neurons are chosen as basic variables, the model of neural networks can be classified into static neural networks or local field networks

Summary

Introduction

Neural networks (NNs) have attracted a great deal of attention because of their extensive applications in various fields such as associative memory, pattern recognition, combinatorial optimization, adaptive control, etc. [ , ]. Among them H∞ state estimation of static neural networks with time delay was studied in [ , – ]. The exponential state estimation of time-varying delayed neural networks was studied in [ ]. These literatures all use the Lyapunov-Krasovskii functionals (LKFs) method, conservativeness comes from two things: the choice of functional and the bound on its derivative. If < , the state estimator for the static neural network has the prescribed H∞ performance and guarantees the globally exponentially stable of the error system. It shows that the delay partitioning method can reduce the conservatism effectively

Methods

Conclusions