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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 340890, 9 pages
http://dx.doi.org/10.1155/2013/340890
Research Article

Network-Based Filter Design for Linear System with Random Delays

1School of Management, Shanghai University of Engineering Science, Shanghai 201620, China
2Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210046, China

Received 9 January 2013; Accepted 13 February 2013

Academic Editor: Yang Tang

Copyright © 2013 Ruixia Yan 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

This paper investigates the filtering problem for a class of network-based systems with random network-induced delays. The considered random delay between the sensor and the filter is assumed to be satisfying a certain stochastic characteristic. Considering the probability of the delay taking value in different intervals, a stochastic variable satisfying Bernoulli random binary distribution is introduced and a new system model is established by employing the information of the probability distribution. By using a properly constructed Lyapunov function, sufficient conditions for the existence of the filters are presented in terms of linear matrix inequalities, which are dependent on the occurrence probability of both the random communication delays. The filter parameter is then characterized by the solution to a set of LMIs. A simulation example is employed to show the effectiveness of the proposed method.