Robust stabilization and H(∞) controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties.

This paper deals with the problem of stabilization design and H(∞) control for a class of genetic regulatory networks (GRNs) with both intrinsic perturbation and extrinsic perturbation. Some delay-dependent mean-square stabilization criteria are put forward for nominal systems and uncertain systems by using an improved free-weighting matrix approach. As a result, the corresponding stabilization controllers and H(∞) controllers of GRNs are constructed with time delays compensated and suboptimal solutions are obtained via exploiting an iterative procedure together with the linear matrix inequality (LMI) method and the cone complementarity liberalization (CCL) algorithm. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.