Finite Time Stability Analysis And Observer Design For Reaction-diffusion Time-delay Gene Regulatory Networks

Genetic regulatory network(GRN)is a mechanism to control gene expression in an organism.Due to the significance of relevant biological background and ge-netic engineering,the extensive study of GRNs has attracted attentions of many academics and others.In this thesis,stability analysis and state observer design problems for a class of GRNs with time-varying delays and reaction-diffusion terms are studied.First,under Dirichlet boundary conditions,delay-dependent and delay-rate-dependent asymptotic stability criteria and finite-time stability criteria for delayed GRNs with reaction-diffusion terms are established by constructing a Lyapunov-Krasovskii functional including quad-slope integrations,and by employing the Jensen inequality,Wirtinger-typeintogral inequality,Gronwall inequality,convex technique and reciprocally convex technique.Numerical examples are provided to illustrate the effectiveness of the theoretical results.Second,under Dirichlet boundary conditions,state observer design problems for a class of GRNs with time-varying delays and reaction-diffusion terms are inves-tigated,which are used to estimate the concentrations of mRNAs and proteins via available measurement outputs.Based on the stability analysis results obtained pre-viously,we establish reaction-diffusion-dependent and delay-dependent asymptotic stability and finite-time stability criteria for the error systems.The stability criteria are 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 full-order or reduced-order state observer gains can be represented by a feasible solution of the set of LMIs.Numerical examples are presented to illustrate the effectiveness of the theoretical results.