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Abstract and Applied Analysis
Volume 2014, Article ID 257971, 12 pages
http://dx.doi.org/10.1155/2014/257971
Research Article

Filtering for Discrete-Time Genetic Regulatory Networks with Random Delay Described by a Markovian Chain

School of Mathematical Science, Heilongjiang University, Harbin 150080, China

Received 14 December 2013; Accepted 22 January 2014; Published 2 March 2014

Academic Editor: Xiaojie Su

Copyright © 2014 Yantao Wang 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 is concerned with the filtering problem for a class of discretetime genetic regulatory networks with random delay and external disturbance. The aim is to design filter to estimate the true concentrations of mRNAs and proteins based on available measurement data. By introducing an appropriate Lyapunov function, a sufficient condition is derived in terms of linear matrix inequalities (LMIs) which makes the filtering error system stochastically stable with a prescribed disturbance attenuation level. The filter gains are given by solving the LMIs. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed approach; that is, our approach is available for a smaller disturbance attenuation level than one in (Liu et al., 2012).