Copyright © 2013 Ruofeng Rao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The robust exponential stability of delayed fuzzy
Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with
nonlinear -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 , Itô formula, Dynkin formula,
the semi-martingale convergence theorem, Schur Complement Theorem, and LMI
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
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