Stability Analysis And Filter Design Of A Kind Of Random Gene Regulatory Network

In this thesis,the stability analysis and filter design for a class of stochastic genetic regulatory networks are studied.The main works of this thesis are as follows:Firstly,by using the existing integral inequality technique and Newton-Leibniz formula,the Jensen type stochastic integral inequalities and the improved stochastic integral inequalities for multiple integrals are given.The improved stochastic integral inequalities are one of the innovation points in this thesis.Secondly,the stability analysis of stochastic genetic regulatory networks with mixed time-varying delays is investigated.By constructing Lyapunov–Krasovskii functional associated with multiple integral terms and using the obtained stochastic integral inequalitis and the(reciprocal)convex combination technique,the meansquare asymptotic stability criteria corresponding to the Jensen type and the improved stochastic integral inequality are presented,respectively.Finally,the simulation results of several numerical examples are provided to verify the effectiveness and less conservativeness of the proposed stability criteria.Thirdly,the filter design of uncertain stochastic genetic regulatory networks with mixed time-varying delays is researched.Based on the stability criteria,the design method of filters without uncertain parameters and with uncertain parameters is given by using matrix analysis technique.Finally,the simulation results of numerical examples are given to verify the effectiveness of the proposed design method.