Improved Delay-Dependent Stability Analysis for Neural Networks with Interval Time-Varying Delays

Yan-min Liu,Jun-kang Tian

doi:10.1155/2015/705367

Abstract

The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method. Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach. Moreover, our criteria depend on both the upper and lower bounds on time-varying delay and its derivative, which is different from some existing ones. Finally, a numerical example is given to show the improved stability region of the proposed results.

Highlights

In the past decades, neural networks have been paid much attention due to their strong capability of information processing such as pattern recognition, image processing, fault diagnosis, and associative memories
The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method
Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach

Summary

Introduction

Neural networks have been paid much attention due to their strong capability of information processing such as pattern recognition, image processing, fault diagnosis, and associative memories. In [10], complete delay-decomposing approach was introduced to derive asymptotic stability criterion for neural networks with time-varying delays by using reciprocally convex technique Among those above methods, the delay-partitioning method is proven to be more effective than the free-weighting matrix approach and augmented Lyapunov functional method. By dividing the lower and upper bounds of the time-varying delay and constructing an improved Lyapunov-Krasovskii functional, [16] obtained some delay-dependent stability criteria in terms of LMIs to reduce the conservatism. By considering the sufficient information of neuron activation functions, [17] obtained some improved delay-dependent stability criteria for neural networks with interval time-varying delay. The information between time-varying delay τ(t) and each subinterval is considered adequately, which may play an important role in reducing conservatism of derived results. A numerical example is given to show the effectiveness of the proposed method

Problem Formulation

Main Results

Numerical Examples

Conclusions