Delay-dependent stability for Markovian genetic regulatory networks with time-varying delays

2011 ◽  
Vol 14 (5) ◽  
pp. 1403-1406 ◽  
Author(s):  
Baoyong Zhang ◽  
Shengyuan Xu ◽  
Yuming Chu ◽  
Guangdeng Zong
Keyword(s):  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Time Varying ◽  
Markovian Genetic Regulatory Networks ◽  
Delay Dependent ◽  
Delay Dependent Stability

Robust Stability of Discrete-Time Randomly Switched Delayed Genetic Regulatory Networks with Known Sojourn Probabilities

2016 ◽  
Vol 20 (7) ◽  
pp. 1094-1102 ◽  
Author(s):  
Xiongbo Wan ◽  
◽  
Chuanyu Ren ◽  
Jianqi An
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Regulatory Function ◽  
Time Varying ◽  
Stability Criteria ◽  
Constraint Condition ◽  
Delay Dependent ◽  
Delay Dependent Stability

This study investigates stability problems related to discrete-time randomly switched genetic regulatory networks (GRNs) with time-varying delays. A new discrete-time randomly switched GRN model with known sojourn probabilities is proposed. By utilizing the discrete Wirtinger-based inequality and a newly proposed constraint condition on the feedback regulatory function, which have not been fully used in stability analysis of discrete-time GRNs, we establish delay-dependent stability and robust stability criteria. These criteria possess the sojourn probabilities of randomly switched GRNs. Two numerical examples are provided to demonstrate the effectiveness of the established results.

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.

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