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Computational and Mathematical Methods in Medicine
Volume 2014, Article ID 761562, 7 pages
http://dx.doi.org/10.1155/2014/761562
Research Article

State Observer Design for Delayed Genetic Regulatory Networks

1School of Information, Beijing Wuzi University, Beijing 101149, China
2College of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, Hebei 050061, China
3Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, SK, Canada S7N 5A9
4Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, Canada S7N 5A9

Received 14 March 2014; Accepted 6 May 2014; Published 22 May 2014

Academic Editor: Zhongming Zhao

Copyright © 2014 Li-Ping Tian 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

Genetic regulatory networks are dynamic systems which describe the interactions among gene products (mRNAs and proteins). The internal states of a genetic regulatory network consist of the concentrations of mRNA and proteins involved in it, which are very helpful in understanding its dynamic behaviors. However, because of some limitations such as experiment techniques, not all internal states of genetic regulatory network can be effectively measured. Therefore it becomes an important issue to estimate the unmeasured states via the available measurements. In this study, we design a state observer to estimate the states of genetic regulatory networks with time delays from available measurements. Furthermore, based on linear matrix inequality (LMI) approach, a criterion is established to guarantee that the dynamic of estimation error is globally asymptotically stable. A gene repressillatory network is employed to illustrate the effectiveness of our design approach.