H∞ Sampled-Data Controller Design for Stochastic Genetic Regulatory Networks

Artificially regulating gene expression is an important step in developing new treatment for system-level disease such as cancer. In this paper, we propose a method to regulate gene expression based on sampled-data measurements of gene products concentrations. Inherent noisy behaviour of Gene regulatory networks are modeled with stochastic nonlinear differential equation. To synthesize feedback controller, we formulate sampling process as an impulsive system. By using a new Lyapunov function with discontinuities at sampling times, state feedback gain that guarantees exponential meansquare stability and H∞ performance is derived from LMIs. These LMIs also determine the maximum allowable time between sampling points. A numerical example and a practical application are presented to justify the applicability of the theoretical results.