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2013 LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion
Ruofeng Rao, Xiongrui Wang, Shouming Zhong, Zhilin Pu
J. Appl. Math. 2013: 1-21 (2013). DOI: 10.1155/2013/396903

Abstract

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω), Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

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Ruofeng Rao. Xiongrui Wang. Shouming Zhong. Zhilin Pu. "LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion." J. Appl. Math. 2013 1 - 21, 2013. https://doi.org/10.1155/2013/396903

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.93092
MathSciNet: MR3064876
Digital Object Identifier: 10.1155/2013/396903

Rights: Copyright © 2013 Hindawi

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