State estimation for delayed genetic regulatory networks with reaction diffusion terms and Markovian jump

Abstract

Abstract Robust state estimation for delayed genetic regulatory networks with reaction–diffusion terms and uncertainties terms under Dirichlet boundary conditions is addressed in this article. The main purpose of the problem investigation is to design a novel state observer for estimate the true concentrations of mRNA and protein by available measurement outputs. Based on Lyapunov–Krasovskii functions and linear matrix inequalities (LMI), sufficient conditions are given to ensure the robust stability of the estimation error networks. Two examples are presented to illustrate the effectiveness of the proposed approach.

Keywords

• Genetic regulatory networks
• Dirichlet boundary
• State estimation
• Reaction–diffusion
• Markov jumping
• Parameter uncertain