Improved asymptotical stability criteria for static recurrent neural networks

Abstract

In this paper, the problem of asymptotical stability for static recurrent neural networks is investigated. Based on delay partitioning approach and a new Lyapunov–Krasvoskii functional, delay-independent conditions are proposed to ensure the asymptotic stability of the static recurrent neural networks. The delay-independent conditions are less conservative than the existing ones. Expressed in linear matrix inequalities, the stability conditions can be checked using the standard numerical software. Two numerical examples are provided to illustrate the effectiveness and the reduced conservatism of the proposed results.

Keywords:

• global asymptotical stability
• linear matrix inequality (LMI)
• Lyapunov–Krasvoskii functional
• delay partitioning approach
• recurrent neural network

2000 AMS Subject Classifications :

• 34D20
• 37C75
• 39A11
• 70K20
• 93D09

Acknowledgements

This work is partly supported by the Nature Science Foundation of Chongqing (CSTC, 2009BB2378, 2008BB2199).