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Robust delay‐probability‐distribution‐dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays
Author(s) -
Wang Wenqin,
Zhong Shouming,
Liu Feng,
Cheng Jun
Publication year - 2013
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.3011
Subject(s) - lemma (botany) , upper and lower bounds , stability (learning theory) , mathematics , discrete time and continuous time , control theory (sociology) , distribution (mathematics) , computer science , mathematical optimization , control (management) , statistics , machine learning , artificial intelligence , mathematical analysis , ecology , poaceae , biology
SUMMARY This study is concerned with the problem of robust delay‐probability‐distribution‐dependent stability of uncertain stochastic genetic regulatory networks with mixed time‐varying delays. The parameter uncertainties are modeled as having a structured linear fractional form. Besides, we consider that the derivatives of the discrete time delays have different upper bounds in various delay intervals. Moreover, less conservative conditions are obtained by choosing an augmented novel Lyapunov–Krasovskii functional and using the lower bound lemma together with the Jensen inequality lemma. Furthermore, the criteria can be applicable to both fast and slow time‐varying delays. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.