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Journal of Applied Mathematics
Volume 2013, Article ID 659251, 10 pages
Research Article

Exponential Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations

1Sichuan Provincial key Lab of Power System Wide-Area Measurement and Control, University of Electronic Science and Technology of China, Chengdu 611731, China
2School of Mathematics and Physics, Chongqing University of Science and Technology, Chongqing 401331, China

Received 12 August 2013; Revised 21 November 2013; Accepted 28 November 2013

Academic Editor: Weihai Zhang

Copyright © 2013 Zhaohui Chen and Qi Huang. 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 delay-dependent exponential performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs). By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed performance . Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.