On delayed uncertain genetic regulatory networks: robust stability analysis

Abstract

In this paper, the problem of stability analysis for uncertain genetic regulatory networks with time-varying delays is investigated. The time-varying delay function in this paper is not required to be either continuously differentiable, or its derivative less than one. By choosing an appropriate Lyapunov–Krasovskii functional and employing some free-weighting matrices, some new delay-dependent and delay-derivative-dependent stability criteria are presented in terms of linear matrix inequality. And the new criteria are applicable to both fast and slow time-varying delays. Finally, three numerical examples are used to demonstrate the usefulness of the main results and less conservativeness of the proposed method.

Keywords:

• genetic regulatory networks
• uncertain system
• robust stability
• time-varying delays
• linear matrix inequality

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). The authors thank the reviewers and the editor for their helpful comments and valuable suggestions.