Regulation of protein expression in cellular level are so challenging. In cellular scale, biochemical processes are intrinsically noisy and many convenient controllers aren’t physically implementable.

In this paper, we consider standard Lyapunov function and by using Ito formula and stochastic analysis, we derive sufficient conditions for noise to state stability presented in the form of matrix inequalities. In the next step, by defining appropriate change of variables, matrix inequalities are transformed to Linear matrix inequalities which can be used to synthesize controller with the desired structure.

This paper deals with the design of implementable controller for stochastic gene regulatory networks with multiplicative and additive noises. In particular, we consider structural limitations that are present in real cellular systems and design the decentralized feedback that guarantees noise to state stability. Since the proposed conditions for controller design are in the form of linear matrix inequalities, controller gains can be derived efficiently through solving presented LMIs numerically. It is noteworthy that Because of its simple structure, the proposed controller can be implemented universally in many cells. Moreover, we consider a synthetic gene regulatory networks and investigate the effectiveness of the proposed controller by simulations.

Our results provide a new method for designing Decentralized controller in gene regulatory networks with intrinsic and extrinsic noises. the proposed controller can be easily implemented in cellular environment.