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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/4089

Title: On robust stability of stochastic genetic regulatory networks with time delays: A delay fractioning approach
Authors: Wang, Y
Wang, Z
Liang, J
Keywords: Genetic Regulatory Networks (GRNs)
Lyapunov–Krasovskii Functional
Linear Matrix Inequality (LMI)
Robust Stability
Stochastic Perturbation
Time Delays
Uncertain System
Publication Date: 2009
Publisher: IEEE
Citation: Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on. 40 (3) 729-740
Abstract: Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of “delay fractioning”, we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures.
Description: Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
URI: http://bura.brunel.ac.uk/handle/2438/4089
DOI: http://dx.doi.org/10.1109/TSMCB.2009.2026059
ISSN: 1083-4419
Appears in Collections:School of Information Systems, Computing and Mathematics Research Papers
Computer Science

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