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Robust H ∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise
Author(s) -
Pan Wei,
Wang Zidong,
Gao Huijun,
Li Yurong,
Du Min
Publication year - 2010
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1571
Subject(s) - multiplicative function , control theory (sociology) , controller (irrigation) , multiplicative noise , noise (video) , gene regulatory network , stochastic control , stochastic process , computer science , stability (learning theory) , process (computing) , synthetic biology , control (management) , mathematical optimization , mathematics , optimal control , biology , gene , transmission (telecommunications) , artificial intelligence , bioinformatics , statistics , signal transfer function , analog signal , image (mathematics) , mathematical analysis , telecommunications , gene expression , operating system , biochemistry , machine learning , agronomy
Abstract Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean‐square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three‐gene network to illustrate the applicability and usefulness of the design. Copyright © 2010 John Wiley & Sons, Ltd.