Delay Stochastic Gene Regulatory Networks Stability Criterion Theoretical Analysis

In this thesis, the problem of stability analysis for genetic regulatory networks(GRNs) with time-varying delays and stochastic disturbances is concerned. Themain research work includes the following two aspects:Firstly, by introducing appropriate Lyapunov-Krasovskii functionals and em-ploying free-weighting matrix approach, Jensen inequality approach, convex combi-nation approach and delay-range partition approach, respectively, some new stabilitycriteria are established to guarantee the considered GRNs to be asymptotically sta-ble in the mean square sense. The stability criteria are given in the form of linearmatrix inequalities (LMIs), which can be easily tested by the YALMIP Toolbox ofMATLAB. Moreover, the rate of change of time-varying delays are assumed to beless than any constant. So, these stability criteria are applicable to both fast andslow changes of time-varying delays;Secondly, we introduced some typical stability criteria in literature, and gavetheoretical comparison on conservativeness of these existing stability criteria withones established in this paper. It turned out that our results are less conservative.Moreover, numerical comparisons are given to evaluate the conservativeness of theseproposed stability criteria. Theoretical comparisons make up for the shortcomingsof numerical comparisons, and make conservativeness analysis of stability criteriafor GRNs more scientifc and reasonable.