Stochastic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters

Abstract

In this paper, the global robust stability of uncertain recurrent neural networks with Markovian jumping parameters which are represented by the Takagi–Sugeno fuzzy model is considered. A novel linear matrix inequality-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in Arik [On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circ. Syst. I 47 (2000), pp. 571–574], Cao [Global stability conditions for delayed CNNs, IEEE Trans. Circ. Syst. I 48 (2001), pp. 1330–1333] and Lou and Cui [Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, J. Math. Anal. Appl. 328 (2007), pp. 316–326] to show the effectiveness and conservativeness.

Keywords:

• Lyapunov functional
• linear matrix inequality
• Markovian jumping parameters
• recurrent neural networks
• T–S fuzzy model

2000 AMS Subject Classifications :

• 34K20
• 34K50
• 92B20
• 94D05

Acknowledgements

The authors are grateful to the editor and the anonymous reviewers for their valuable comments and suggestions. The work was supported by NBHM project grant No.48/1/2007/-RD-II/7446.