Delay dependent robust stability of genetic regulatory networks with time varying delays

2011 ◽  
Author(s):  
Rubei Zhang ◽  
Yutian Zhang ◽  
Yan Yuan
Keyword(s):  
Robust Stability ◽  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Time Varying ◽  
Delay Dependent

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.

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

scholarly journals An advanced delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays

2018 ◽  
Vol 23 (6) ◽  
pp. 803-829 ◽  
Author(s):  
Selvakumar Pandiselvi ◽  
Raja Ramachandran ◽  
Jinde Cao ◽  
Grienggrai Rajchakit ◽  
Aly R. Seadawy ◽  
...  
Keyword(s):  
Regulatory Networks ◽  
Convex Combination ◽  
Genetic Regulatory Networks ◽  
Distributed Delays ◽  
Combination Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Theoretical Concepts ◽  
Delay Dependent

In this typescript, we concerned the problem of delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays. An advanced Lyapunov–Krasovskii functional are defined, which is in triple integral form. Combining the Lyapunov–Krasovskii functional with convex combination method and free-weighting matrix approach the stability conditions are derived with the help of linear matrix inequalities (LMIs). Some available software collections are used to solve the conditions. Lastly, two numerical examples and their simulations are conferred to indicate the feasibility of the theoretical concepts.

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
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