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Complexity
Volume 2017, Article ID 4573039, 17 pages
https://doi.org/10.1155/2017/4573039
Research Article

Design of Nonfragile State Estimator for Discrete-Time Genetic Regulatory Networks Subject to Randomly Occurring Uncertainties and Time-Varying Delays

1College of Automation, Harbin Engineering University, Harbin 150001, China
2Graduate Department, Harbin University of Science and Technology, Harbin 150080, China
3College of Science, Harbin Engineering University, Harbin 150001, China
4College of Science, Harbin University of Science and Technology, Harbin 150080, China

Correspondence should be addressed to Yanfeng Zhao; nc.ude.tsubrh@gnefnayoahz

Received 10 March 2017; Accepted 21 May 2017; Published 2 October 2017

Academic Editor: Dimitri Volchenkov

Copyright © 2017 Yanfeng Zhao 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

We deal with the design problem of nonfragile state estimator for discrete-time genetic regulatory networks (GRNs) with time-varying delays and randomly occurring uncertainties. In particular, the norm-bounded uncertainties enter into the GRNs in random ways in order to reflect the characteristic of the modelling errors, and the so-called randomly occurring uncertainties are characterized by certain mutually independent random variables obeying the Bernoulli distribution. The focus of the paper is on developing a new nonfragile state estimation method to estimate the concentrations of the mRNA and the protein for considered uncertain delayed GRNs, where the randomly occurring estimator gain perturbations are allowed. By constructing a Lyapunov-Krasovskii functional, a delay-dependent criterion is obtained in terms of linear matrix inequalities (LMIs) by properly using the discrete-time Wirtinger-based inequality and reciprocally convex combination approach as well as the free-weighting matrix method. It is shown that the proposed method ensures that the estimation error dynamics is globally asymptotically stable and the desired estimator parameter is designed via the solutions to certain LMIs. Finally, we provide two numerical examples to illustrate the feasibility and validity of the proposed estimation results.