Impulsive control strategies of mRNA and protein dynamics on fractional-order genetic regulatory networks with actuator saturation and its oscillations in repressilator model.

In genetic regulatory networks (GRNs), the control strategies of messenger RNA (mRNA) and protein play a key role in regulatory mechanisms of gene expression, especially in translation and transcription. However, the influence of impulsive control strategies on oscillatory gene expression is not well understood. In this article, by considering the impulsive control strategies of mRNA and protein, a novel fractional-order genetic regulatory networks with actuator saturation is proposed. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequalities (LMIs) criteria that guarantee finite-time Mittag-Leffler stabilization problem for fractional-order genetic regulatory networks are given. The derived sufficient conditions can easily be verified by designing impulsive control gains and solving simple LMIs. Finally, to investigate the effectiveness and applicability of the control strategies, an interesting simulation example as a synthetic oscillatory network of transcriptional regulators in Escherichia coli is illustrated.