New LMI-based Criteria for Lagrange Stability of Cohen-Grossberg Neural Networks with General Activation Functions and Mixed Delays

Huan Qi,Xiaohong Wang

doi:10.1080/18756891.2013.805587

Abstract

Abstract In this paper, the problem on Lagrange stability of Cohen-Grossberg neural networks (CGNNs) with both mixed delays and general activation functions is considered. By virtue of Lyapunov functional and Halanay delay differential inequality, several new criteria in linear matrix inequalities (LMIs) form for the global exponential stability in Lagrange sense of CGNNs are obtained. Meanwhile, the limitation on the activation functions being bounded, monotonous and differentiable is released, which generalizes and improves those existent results. Moreover, detailed estimations of the globally exponentially attractive sets are given out. It is also verified that outside the globally exponentially attractive set, there is no equilibrium state, periodic state, almost periodic state, and chaos attractor of the CGNNs. Finally, two numerical examples are given to demonstrate the theoretical results.

Highlights

Since the discovery of the Cohen-Grossberg neural networks (CGNNs) [1] in 1983, a lot of applications have been appeared in many fields to solve control, signal processing, associative memory, parallel computation and nonlinear optimization problems
Under assumption (A), the CGNNs system (1) is globally exponentially stable in Lagrange sense if there exist five positive diagonal matrices P, Q, R, S, T and a positive definite matrix H ∈ Rn×n such that the following linear matrix inequalities (LMIs) hold:
The CGNNs system (1) is globally exponentially stable in Lagrange sense if there exist four positive diagonal matrices P, Q, R, S and a positive definite matrix H ∈ Rn×n such that the following LMIs hold:

Summary

Introduction

Since the discovery of the Cohen-Grossberg neural networks (CGNNs) [1] in 1983, a lot of applications have been appeared in many fields to solve control, signal processing, associative memory, parallel computation and nonlinear optimization problems. From a dynamical system point of view, globally stable networks in Lyapunov sense are monostable systems, which have a unique equilibrium attracting all trajectories asymptotically. Monostable neural networks have been found computationally restrictive and multistable dynamics are essential to deal with important neural computations desired.

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Conclusion