State Estimation for Gene Regulatory Networks with Sampled Output Measurements and Time-varying Delays

This paper investigates the H∞ state estimation problem for gene regulatory networks (GRNs) with timevarying delays and Markovian jumping parameters. The system output, which is used by the estimator, is assumed to be sampled and held during a sampling period. To deal with the time-varying delays, each delay function is limited to certain lower and upper bounds. By using Lyapunov-Krasovskii functionals, sufficient conditions for the stochastic stability of augmented GRN/Estimator networks are derived. Then, the estimator gains are synthesized from the derived stability conditions. Furthermore, we investigate how to design the estimator in presence of disturbance. All stability conditions are formulated in the form of linear matrix inequalities which can be easily solved by numerical methods. The obtained conditions are dependent on both the lower and upper bounds of delays. At the end, some simulation results are presented to demonstrate the effectiveness of the proposed method.