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Zbl 1221.34189
Ali, M.Syed; Balasubramaniam, P.
Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 7, 2907-2916 (2011). ISSN 1007-5704

Summary: The Takagi--Sugeno (T--S) fuzzy model representation is extended to the stability analysis for stochastic cellular neural networks with multiple discrete and distributed time varying delays. A novel Linear Matrix Inequality (LMI) based stability criterion is derived to guarantee the asymptotic stability of stochastic cellular neural networks with multiple discrete and distributed time varying delays which are represented by T--S fuzzy models. The derived delay-dependent stability conditions are based on free-weighting matrices method, Lyapunov's stability theory and LMI technique. In fact, these techniques lead to a generalized and less conservative stability condition that guarantee the wide stability region. The delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay is removed. Our results can be specialized to several cases including those studied extensively in the literature. Finally, numerical examples are given to demonstrate the effectiveness and conservativeness of our results.
MSC 2000:
*34K20 Stability theory of functional-differential equations
34K36
34K50 Stochastic delay equations
92B20 General theory of neural networks

Keywords: cellular neural networks; global asymptotic stability; linear matrix inequality; Lyapunov functional; multiple discrete and distributed time-varying delays; stochastic systems; T--S fuzzy model

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