Stochastic asymptotic boundedness of genetic regulatory networks

Due to the randomness of the biochemical process at the molecular level, genetic regulatory networks are inherently noisy. They are also subjected to extrinsic noises which are external to the gene expression. In this paper, we consider genetic regulatory networks with non-vanishing additive noises and investigate stochastic asymptotic boundedness of them. By using itô´s differential formula and Lyapunov-Krasovskii functional, we derive sufficient conditions so that system solution be bounded (in expectation) by a monotone function of the supremum of the covariance of the noise. All these conditions are presented in terms of linear matrix inequalities (LMIs). Finally, Numerical example illustrates the usefulness and applicability of the proposed conditions.