Mean Square Exponential Stability of Stochastic Cohen-Grossberg Neural Networks with Unbounded Distributed Delays

Discrete Dynamics in Nature and Society (Impact Factor: 0.88). 01/2010; 2010(1026-0226). DOI: 10.1155/2010/513218
Source: DOAJ

ABSTRACT This paper addresses the issue of mean square
exponential stability of stochastic Cohen-Grossberg neural
networks (SCGNN), whose state variables are described by
stochastic nonlinear integrodifferential equations. With the
help of Lyapunov function, stochastic analysis technique, and
inequality techniques, some novel sufficient conditions on mean
square exponential stability for SCGNN are given. Furthermore,
we also establish some sufficient conditions for checking
exponential stability for Cohen-Grossberg neural networks with
unbounded distributed delays.

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    ABSTRACT: This paper is concerned with the exponential stability problem for a class of stochastic Cohen–Grossberg neural networks with discrete and unbounded distributed time delays. By applying the Jensen integral inequality and the generalized Jensen integral inequality, several improved delay-dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results.
    Neural Processing Letters 04/2011; 35(2). DOI:10.1007/s11063-011-9206-9 · 1.45 Impact Factor


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