Novel passivity criteria for neural networks with discrete and unbounded distributed time-varying delays

Abstract

Novel passivity criteria are presented for the passivity of a class of cellular neural networks with discrete and unbounded distributed time-varying delays. Two types of uncertainty are considered: one is time-varying structured uncertainty while the other is interval uncertainty. The Gu's discretized Lyapunov–Krasovskii functional method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz–Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for passivity of delayed neural networks. A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing passivity criteria.

Keywords:

• passivity
• linear matrix inequality
• cellular neural networks
• argumented Lyapunov–Krasovskii functional
• interval uncertainty

2010 AMS Subject Classifications :

• 34A34
• 34D23
• 34K20
• 92B20
• 93D05

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 50977008, 60821063, 61034005, 61273022, National Basic Research Program of China (2009CB320601), and by the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 200801451096, by the China Postdoctoral Science Foundation under Grants 20080431150 and 200902547.