scholarly journals An r-Order Finite-Time State Observer for Reaction-Diffusion Genetic Regulatory Networks with Time-Varying Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaofei Fan ◽  
Yantao Wang ◽  
Ligang Wu ◽  
Xian Zhang
Keyword(s):  
Finite Time ◽  
Regulatory Networks ◽  
Reaction Diffusion ◽  
State Observer ◽  
Genetic Regulatory Networks ◽  
Dirichlet Boundary Conditions ◽  
Time Varying ◽  
Error System ◽  
Delay Dependent ◽  
T State

It will be settled out for the open problem of designing an r-order finite-time (F-T) state observer for reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays. By assuming the Dirichlet boundary conditions, aiming to estimate the mRNA and protein concentrations via available network measurements. Firstly, sufficient F-T stability conditions for the filtering error system have been investigated via constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using several integral inequalities and (reciprocally) convex technique simultaneously. These conditions are delay-dependent and reaction-diffusion-dependent and can be checked by MATLAB toolbox. Furthermore, a method is proposed to design an r-order F-T state observer, and the explicit expressions of observer gains are given. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.

scholarly journals Finite-Time Robust Stability of Uncertain Genetic Regulatory Networks with Time-Varying Delays and Reaction-Diffusion Terms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Wenqin Wang ◽  
Yali Dong ◽  
Shouming Zhong ◽  
Feng Liu
Keyword(s):  
Robust Stability ◽  
Integral Inequality ◽  
Finite Time ◽  
Regulatory Networks ◽  
Reaction Diffusion ◽  
Genetic Regulatory Networks ◽  
Green Formula ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Stability Criteria

This study seeks to address the finite-time robust stability of delayed genetic regulatory networks (GRNs) with uncertain parameters and reaction-diffusion terms. We employ an appropriate Lyapunov-Krasovskii functional to derive some less conservative stability criteria for GRNs under Dirichlet boundary conditions, which are delay-dependent, delay-derivative-dependent, and reaction-diffusion-dependent. The time-varying delays and their derivatives are both bounded with lower and upper bounds, where the lower bound of them can be zero or non-zero. In addition, we define some new variables to deal with uncertain parameters. Moreover, Jensen’s integral inequality, Wirtinger-type integral inequality, reciprocally convex combination inequality, Gronwall inequality, and Green formula are employed to handle integral terms. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the obtained stability criteria.

Passivity of Reaction–Diffusion Genetic Regulatory Networks with Time-Varying Delays

2017 ◽  
Vol 47 (3) ◽  
pp. 1115-1132 ◽  
Author(s):  
Chengye Zou ◽  
Xiaopeng Wei ◽  
Qiang Zhang ◽  
Changjun Zhou
Keyword(s):  
Regulatory Networks ◽  
Reaction Diffusion ◽  
Genetic Regulatory Networks ◽  
Time Varying
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