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

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.

Keywords

• Cohen-Grossberg neural networks
• Lagrange stability
• Globally exponentially attractive set
• Linear matrix inequality(LMI)
• Time-varying delays and finite distributed delays