Filter Designed With Varying Time Delays Discrete Gene Regulatory Networks

This thesis studies the fltering problem for two classes of discrete-time geneticregulatory networks with time-varying delays. We mainly research the following twoaspects:Firstly, the problem of H∞flter for discrete-time genetic regulatory networkswith random delay and external disturbance is considered. The aim to, based onavailable measurement data, design an H∞flter to estimate the true concentra-tions of mRNAs and proteins. By introducing an appropriate Lyapunov function,a sufcient condition in the form of linear matrix inequalities (LMIs) is derived tomake the fltering error system to be stochastically stable with a prescribed H∞dis-turbance attenuation level. The flter gain matrices are given by solving the LMIs.A scalar γ can be calculated as an optimization variable to obtain a minimum ofthe H∞disturbance attenuation level. Based on simulation results of a numericalexample, the theory results is verifed to be valid and correct.Secondly, the problem of exponential passive fltering for discrete-time genet-ic regulatory networks with random discrete delay and constant distributed delayis considered. First of all, by introducing an appropriate Lyapunoy function, asufcient condition is presented to ensure the fltering error system to be strictlyexponentially passive with dissipation γ>0. In the next place, based on availablemeasurement date, an exponential passive flter is designed to estimate the true con-centrations of mRNAs and proteins. Finally, a numerical example and its simulationresults are given to illustrate the efectiveness of the proposed exponential passivefltering approach.