Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 524187, 17 pages
http://dx.doi.org/10.1155/2012/524187
Research Article

Stability Analysis for Stochastic Markovian Jump Reaction-Diffusion Neural Networks with Partially Known Transition Probabilities and Mixed Time Delays

Weiyuan Zhang,1,2 Junmin Li,1 and Naizheng Shi1

1School of Science, Xidian University, Shaanxi, Xi'an 710071, China
2Institute of Mathematics and Applied Mathematics, Xianyang Normal University, Shaanxi, Xianyang 712000, China

Received 11 January 2012; Accepted 28 February 2012

Academic Editor: Josef Diblík

Copyright © 2012 Weiyuan Zhang 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.

Abstract

The stability problem is proposed for a new class of stochastic Markovian jump reaction-diffusion neural networks with partial information on transition probability and mixed time delays. The new stability conditions are established in terms of linear matrix inequalities (LMIs). To reduce the conservatism of the stability conditions, an improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. The obtained results are dependent on delays and the measure of the space AND, therefore, have less conservativeness than delay-independent and space-independent ones. An example is given to show the effectiveness of the obtained results.