Sampled-Data State Estimation of Reaction Diffusion Genetic Regulatory Networks via Space-Dividing Approaches

A novel state estimator is designed for genetic regulatory networks with reaction-diffusion terms in this study. First, the diffusion space (where mRNA and protein exist) is divided into several parts and only a point, a line, or a plane, etc., is measured in every subspace to reduce the measurement cost effectively. Then, samplers and network-induced time delay are considered to meet the network transmission requirement. A new criterion to ensure that the estimation error converges to zero is established by using the Lyapunov functional combined with Wirtinger's inequality, reciprocally convex approach, and Halanay's inequality; furthermore, the estimator's parameters are derived by solving linear matrix inequalities. Finally, two simulation examples (including one-dimensional and two-dimensional spaces) are presented to demonstrate the developed scheme's applicability.

Automated summary

A novel state estimator for genetic regulatory networks with reaction-diffusion terms was designed in this study, where the diffusion space is divided into parts for cost reduction and samplers and network-induced time delay are considered. The convergence to zero of estimation error is ensured through a new criterion using various mathematical tools, and linear matrix inequalities are used to derive the estimator's parameters. Two simulation examples are presented to showcase the applicability of the developed scheme in one-dimensional and two-dimensional spaces.