Robust H∞H∞ observer-based controller for stochastic genetic regulatory networks

• An observer based controller for genetic regulatory networks is presented.
• The controller guarantees asymptotically stability in the mean square sense.
• The controller achieves the prescribed H∞ disturbance attenuation level.
• A case study demonstrates the effectiveness of the proposed methods.

This study is considered with the robust H∞H∞ observer based controller problem for a nonlinear genetic regulatory network (GRN) includes noise and disturbances, delays, and parameter uncertainties. The nonlinear functions describing the feedback regulation are assumed to satisfy the sector-like conditions; the parameter uncertainties are time-varying and unknown but are norm-bounded, and the delays are time-varying. We aim to design robust observer based controller to stabilize the stochastic GRN such that, for all admissible uncertainties, nonlinearities, stochastic perturbations and time varying delays, the dynamics of the GRN and observer are guaranteed to be robustly asymptotically stable in the mean square sense while achieving the prescribed H∞H∞ disturbance attenuation level. Based on the Lyapunov method and the stochastic analysis technique, it is shown that if a set of linear matrix inequalities (LMIs) are feasible, the desired observer based controller does exist. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.