Further stability analysis on Cohen–Grossberg neural networks with time-varying and distributed delays

Abstract

The article is concerned with asymptotical stability for Cohen–Grossberg neural networks with both interval time-varying (0 ≤ τ₀ ≤ τ(t) ≤ τ _m ) and distributed delays, in which two types of distributed delays are treated: one is bounded while the other is unbounded. Through partitioning the delay intervals [0, τ₀] and [τ₀, τ _m ], and choosing two augmented Lyapunov–Krasovskii functionals, some sufficient conditions are obtained to guarantee the global stability by employing the simplified free-weighting matrix method and convex combination. These stability criteria are presented in terms of linear matrix inequalities (LMIs) and can be easily checked by resorting to LMI in Matlab toolbox. Finally, three numerical examples are given to illustrate the effectiveness and reduced conservatism of the theoretical results.

Keywords:

• global stability
• Cohen–Grossberg neural networks (CGNNs)
• time delay
• distributed delay
• LMI approach

Acknowledgements

The authors thank the editor and reviewers for their constructive comments for improving the quality of this article. This work is supported by the National Natural Science Foundation of China, Grant Nos. 60764001, 60835001, 60875035, 60904023 and 61004032, National High Technology Research and Development Programme 863 No. 2009AA012311, Jiangsu Planned Projects for Postdoctoral Research Funds, No. 0901005B and China Postdoctoral Science Foundation Funded Project, No. 200904501033.