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| Delay-Dependent Exponential Stability for NonlinearReaction-Diffusion Uncertain Cohen-Grossberg NeuralNetworks with Partially Known TransitionRates via Hardy-Poincar′e Inequality |
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Citation： |
Ruofeng RAO.Delay-Dependent Exponential Stability for NonlinearReaction-Diffusion Uncertain Cohen-Grossberg NeuralNetworks with Partially Known TransitionRates via Hardy-Poincar′e Inequality[J].Chinese Annals of Mathematics B,2014,35(4):575~598 |
| Page view： 1243
Net amount： 1081 |
Authors： |
Ruofeng RAO; |
Foundation： |
the National Basic Research Program of China (No. 2010CB732501), the
Scientific Research Fund of Science Technology Department of Sichuan Province (Nos. 2010JY0057,
2012JYZ010), the Sichuan Educational Committee Science Foundation (Nos. 08ZB002, 12ZB349) and
the Scientific Research Fund of Sichuan Provincial Education Department (Nos. 14ZA0274, 08ZB002,
12ZB349). |
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| Abstract： |
In this paper, stochastic global exponential stability criteria for delayed impulsive
Markovian jumping reaction-diffusion Cohen-Grossberg neural networks (CGNNs
for short) are obtained by using a novel Lyapunov-Krasovskii functional approach, linear
matrix inequalities (LMIs for short) technique, It?o formula, Poincar′e inequality and
Hardy-Poincar′e inequality, where the CGNNs involve uncertain parameters, partially unknown
Markovian transition rates, and even nonlinear p-Laplace diffusion (p > 1). It is
worth mentioning that ellipsoid domains in Rm (m ≥ 3) can be considered in numerical
simulations for the first time owing to the synthetic applications of Poincar′e inequality and
Hardy-Poincar′e inequality. Moreover, the simulation numerical results show that even the
corollaries of the obtained results are more feasible and effective than the main results of
some recent related literatures in view of significant improvement in the allowable upper
bounds of delays. |
Keywords： |
Hardy-Poincar′e inequality, Laplace diffusion, Linear matrix inequality |
Classification： |
34D20, 34D23 |
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