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Robust stability of Markovian jumping genetic regulatory networks with disturbance attenuation
Author(s) -
Yao Yingtao,
Liang Jinling,
Cao Jinde
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.373
Subject(s) - control theory (sociology) , markov chain , linear matrix inequality , stability (learning theory) , markov process , noise (video) , attenuation , gene regulatory network , lyapunov function , computer science , mode (computer interface) , mathematics , control (management) , mathematical optimization , nonlinear system , physics , gene , biology , artificial intelligence , biochemistry , statistics , gene expression , quantum mechanics , machine learning , optics , image (mathematics) , operating system
Because of intracellular and extracellular noise perturbations and environment fluctuations, gene regulation is an intrinsically noisy process. In this paper, we present a hybrid genetic regulatory network (GRN) model which is based on the Markov chain. The GRNs are composed of N modes and the network switches from one mode to another according to a Markov chain with known transition probability. Time‐delays here are mode‐dependent. Based on the Lyapunov stability theory and the linear matrix inequality (LMI) technique, sufficient conditions are given to ensure the stochastic stability of the GRNs with polytopic uncertainties and disturbance attenuation. All the conditions are presented in terms of LMIs which are easily verified via the LMI toolbox. Examples are provided to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society