State Estimation for Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms

TL;DR

This paper develops a new observer design for genetic regulatory networks with delays and reaction-diffusion effects, ensuring accurate state estimation through Lyapunov-based LMIs and numerical validation.

Contribution

It introduces a novel Lyapunov-Krasovskii functional and stability criteria for state estimation in complex genetic networks with time-varying delays.

Findings

The proposed observer guarantees asymptotic stability under certain delay bounds.

Feasibility of LMIs indicates the existence of the desired observer.

Numerical examples confirm the effectiveness of the method.

Abstract

This paper is concerned with the state estimation problem for genetic regulatory networks with time-varying delays and reaction-diffusion terms under Dirichlet boundary conditions. It is assumed that the nonlinear regulation function is of the Hill form. The purpose of this paper is to design a state observer to estimate the concentrations of mRNA and protein through available measurement outputs. By introducing new integral terms in a novel Lyapunov--Krasovskii functional and employing Wirtinger-based integral inequality, Wirtinger's inequality, Green's identity, convex combination approach, and reciprocally convex combination approach, an asymptotic stability criterion of the error system is established in terms of linear matrix inequalities (LMIs). The obtained stability criterion depends on the upper bounds of the delays and their derivatives. It should be highlight that if the set of LMIs are feasible, the desired observer exists and can be determined. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed designed scheme.