Finite-time state observer for delayed reaction-diffusion genetic regulatory networks

This paper focus on the finite-time state estimation problem for delayed reaction-diffusion genetic regulatory networks (DRDGRNs) under Dirichlet boundary conditions. The purpose is to design a finite-time state observer which is used to estimate the concentrations of mRNAs and proteins via available measurement outputs. By constructing a Lyapunov-Krasovskii functional (LKF) concluding quad-slope integrations, we establish a reaction-diffusion-dependent and delay-dependent finite-time stability criterion for the error system. The derivative of LKF is estimated by employing the Wirtinger-type integral inequality, Gronwall inequality and convex (reciprocally convex) technique. The stability criterion is to check the feasibility of a set of linear matrix inequalities (LMIs), which can be easily realized by the toolbox YALMIP of MATLAB. In addition, the expected finite-time state observer gain matrices can be represented by a feasible solution of the set of LMIs. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.