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This paper investigates the delay-dependent global asymptotic stability problem of stochastic genetic regulatory networks (SGRNs) with Markovian jumping parameters. Based on the Lyapunov–Krasovskii functional and stochastic analysis approach, a delay-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are globally asymptotically stable in the mean square. Distinct difference from other analytical approaches lies in “linearization” of the genetic regulatory networks (GRNs) model, by which the considered GRN model is transformed into a linear system. Then, a process, which is called parameterized first-order model transformation is used to transform the linear system. Novel criteria for global asymptotic stability of the SGRNs with constant delays are obtained. Some numerical examples are given to illustrate the effectiveness of our theoretical results.
Journal: Applied Mathematical Modelling - Volume 36, Issue 4, April 2012, Pages 1718–1730