Robust H feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

Authors

  • Wei Pan,

    1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, People's Republic of China
    2. Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, People's Republic of China
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  • Zidong Wang,

    Corresponding author
    1. School of Information Science and Technology, Donghua University, Shanghai 200051, China
    2. Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, U.K.
    • School of Information Science and Technology, Donghua University, Shanghai 200051, China
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  • Huijun Gao,

    1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, People's Republic of China
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  • Yurong Li,

    1. Department of Electrical Engineering, Fuzhou University, Fuzhou 350002, People's Republic of China
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  • Min Du

    1. Department of Electrical Engineering, Fuzhou University, Fuzhou 350002, People's Republic of China
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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.

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