An LPV based robust peak-to-peak state estimation for genetic regulatory networks with time varying delay

Reduced- and Full-Order Observers for Delayed Genetic Regulatory Networks

This paper is centered upon the state estimation for delayed genetic regulatory networks. Our aim is at estimating the concentrations of mRNAs and proteins by designing reduced-order and full-order state observers based on available network outputs. We introduce a Lyapunov-Krasovskii functional including quadruplicate integrals, and estimate its derivative by employing the Wirtinger-type integral inequalities, reciprocal convex technique, and convex technique. From which, delay-dependent sufficient conditions, in the form of linear matrix inequalities (LMIs), are investigated to ensure that the resultant error system is asymptotically stable. One can verify these conditions by utilizing the MATLAB Toolboxes LMI or YALMIP. In addition, the gains of reduced-order and full-order observers are represented by the feasible solutions of the LMIs, and thereby, the concrete expressions of the desired reduced-order and full-order state observers are presented. Finally, the simulation results of a numerical example are demonstrated, which explains the validity of the proposed method.

State Estimation for Delayed Genetic Regulatory Networks With Reaction-Diffusion Terms

This paper addresses the problem of state estimation for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms using Dirichlet boundary conditions. The nonlinear regulation function of DGRNs is assumed to exhibit the Hill form. The aim of this paper is to design a state observer to estimate the concentrations of mRNAs and proteins via available measurement techniques. By introducing novel integral terms into the Lyapunov-Krasovskii functional and by employing the Wirtinger-type integral inequality, the convex approach, Green's identity, the reciprocally convex approach, and Wirtinger's inequality, an asymptotic stability criterion of the error system was established in terms of linear matrix inequalities (LMIs). The stability criterion depends upon the bounds of delays and their derivatives. It should be noted that if the set of LMIs is feasible, then the desired observation of DGRNs is possible, and the state estimation can be determined. Finally, two numerical examples are presented to illustrate the availability and applicability of the proposed scheme design.