Stability Analysis And Observer Design Of Gene Regulatory Network Based On Model Transformation

This thesis is concerned with the problem of stability analysis for a class of genetic regulatory networks(GRNs)with discrete delays,and the problem of state observer design for a class of GRNs with discrete and leakage delays.In the first part,we address the problem of the asymptotic stability for a class of GRNs with discrete delays.First,the system model is simplified to a reduced-order system with bounded uncertain parameters and distributed delays by exploiting calculus’ s properties and Lagrange’s Mean–Value Theorem.Second,the asymptotic stability problem of the primal systems is transformed into the robust asymptotic stability problem of the reduced-order one.Then,by using Cauchy–Schwarz inequality method,convex combination technique,and Lyapunov–Krasovskii(LK)functional,a stability criterion of the reduced-order system are given.At last,a numerical example illustrates the effectiveness of the proposed method in this paper.In the second part,we investigate the problem of state observer design for a class of GRNs with discrete and leakage delays.The objective is to estimate the system’s total state based on measurable output values.First,by using the Lagrange’s Mean–Value Theorem to deal with the nonlinear terms in the model,we transform the nonlinear error system into a linear one with bounded uncertain items.Second,using LK functional,Barablat lemma,LMI,Jessen inequality and Schur complement technique,etc.the criteria for robust asymptotic stability of error systems are given.Thereby,we can obtain the state observer based on the feasible solution to LMI.At last,the availability of the designed state observer is verified by the simulation results of numerical example.