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.