Delay Stability Analysis Of Gene Regulatory Network

The genetic regulatory networks with time delay embody the rich dynamical actions,which are important parts of the delayed network systems. Over the past several years,owning to the vast applications in bioscience, engineering and other research felds, manyresearchers have devoted to the problem of stability analysis of GRNs and a great numberof results have been reported. A system is often called an interval system if the uncertaintyis only represented by the bounded deviations and perturbations of its parameters. Becauseof the importance in theory and application, the study on the stability of delayed intervalgenetic regulatory networks is becoming more and more important. In this thesis, we mainlyfocus on the stability problem for a class of delayed genetic regulatory networks. Morespecifcally, the main results are listed as follows:1) New delay-dependent stability condition for GRNs with neutral delay.The asymptotic stability problem of genetic regulatory networks(GRNs) with neutraltime-varying/constant delay is considered. The discrete delay may be not diferentiable,which is unnecessarily equal to the neutral delay. By introducing a new Lyapunov-Krasovskiifunction and the free weighting matrix technique, sufcient delay-dependent stability condi-tions are developed and presented in terms of strict linear matrix inequality(LMI), which canbe easily verifed by using the LMI tool-box. Finally, two numerical examples are providedto demonstrate the efectiveness and reduced conservativeness of the proposed algorithm.2) Robust delay-dependent asymptotical stability criteria for interval genetic regulatorynetworks with time-varying delays.We cope with the the delay-dependent robust stability problem for genetic regulato-ry networks with interval uncertainty. By using the free weighting matrix technique andan equivalent transformation of interval systems, delay-dependent and delay-derivative-dependent/independent stability criteria are established. All the conditions presented hereare in the form of linear matrix inequalities (LMIs), which can be easily verifed by usingrecently developed algorithms in solving LMIs. Finally, three numerical examples are givento show the efectiveness and less conservativeness of the proposed algorithm.