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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 103542, 20 pages
http://dx.doi.org/10.1155/2012/103542
Research Article

Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

1Department of Mathematics, Mudanjiang Normal University, Heilongjiang 157012, China
2Department of Applied Mathematics, Yanshan University, Qinhuangdao 066004, China

Received 21 February 2012; Accepted 8 April 2012

Academic Editor: Agacik Zafer

Copyright © 2012 Hongwen Xu 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 interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.