LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion
Joint Authors
Pu, Zhilin
Wang, Xiong Rui
Rao, Ruofeng
Zhong, Shouming
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-26
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Rao, Ruofeng& Wang, Xiong Rui& Zhong, Shouming& Pu, Zhilin. 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. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-21.
https://search.emarefa.net/detail/BIM-468887
Modern Language Association (MLA)
Rao, Ruofeng…[et al.]. LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion. Journal of Applied Mathematics No. 2013 (2013), pp.1-21.
https://search.emarefa.net/detail/BIM-468887
American Medical Association (AMA)
Rao, Ruofeng& Wang, Xiong Rui& Zhong, Shouming& Pu, Zhilin. LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-21.
https://search.emarefa.net/detail/BIM-468887
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468887