A note on the robust stability of genetic regulatory networks with time-varying delays

2008 ◽  
Author(s):  
Wei Feng ◽  
Wei Zhang ◽  
Guangxia Xu ◽  
Haixia Wu
Keyword(s):  
Robust Stability ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Time Varying

Robust stability for uncertain genetic regulatory networks with interval time-varying delays

2010 ◽  
Vol 180 (18) ◽  
pp. 3532-3545 ◽  
Author(s):  
Haixia Wu ◽  
Xiaofeng Liao ◽  
Wei Feng ◽  
Songtao Guo ◽  
Wei Zhang
Keyword(s):  
Robust Stability ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Time Varying ◽  
Interval Time

Robust Stability Analysis for Uncertain Genetic Regulatory Networks with Time-varying Delays

2013 ◽  
Vol 12 (18) ◽  
pp. 4417-4425
Author(s):  
Xinghua Zhang ◽  
Jinmei Xiao ◽  
Shaochun Cui ◽  
Yantao Wang ◽  
Xian Zhang
Keyword(s):  
Stability Analysis ◽  
Robust Stability ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Time Varying ◽  
Robust Stability Analysis

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 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.

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