Robust stabilization and <i>H</i>_∞ control for discrete-time stochastic genetic regulatory networks with time delays

This paper presents some novel results on robust stabilization and H∞ control design for a class of uncertain discrete-time stochastic genetic regulatory networks (GRNs) with time-varying delays. The GRNs under consideration are subject to stochastic noise, time-varying, and norm bounded parameter uncertainties. By constructing a new Lyapunov–Krasovskii functional that contains some novel triple summation terms, we propose a state feedback gene controller to guarantee that the considered GRN is mean-square asymptotically stable about its equilibrium point for all admissible uncertainties. The other issue is to design a H∞ feedback gene controller so that the GRN is robustly stable with a prescribed H∞ disturbance attenuation level for all admissible uncertainties and for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, the control scheme has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained results. </jats:p