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Zbl 1239.92041
Zhang, Wenbing; Fang, Jian-an; Tang, Yang
Robust stability for genetic regulatory networks with linear fractional uncertainties. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 17, No. 4, 1753-1765 (2012). ISSN 1007-5704

Summary: The asymptotic stability analysis problem for a class of delayed genetic regulatory networks (GRNs) with linear fractional uncertainties and stochastic perturbations is studied. By employing a more effective Lyapunov functional and using a lemma to estimate the derivatives of the Lyapunov functional, some new sufficient conditions for the stability problem of GRNs are derived in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are used to demonstrate the usefulness of the main results and less conservatism of the derived conditions.

MSC 2000:: *92C42
34K20 Stability theory of functional-differential equations
15A45 Miscellaneous inequalities involving matrices

Keywords: GRNs; linear matrix inequality (LMI); asymptotic stability; Lyapunov functional; stochastic perturbations

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