scholarly journals Stability of Uncertain Impulsive Stochastic Genetic Regulatory Networks with Time-Varying Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Jun Li ◽  
Manfeng Hu ◽  
Jinde Cao ◽  
Yongqing Yang ◽  
Yinghua Jin
Keyword(s):  
Regulatory Networks ◽  
Convex Combination ◽  
Genetic Regulatory Networks ◽  
Time Varying ◽  
Leakage Term ◽  
Combination Technique ◽  
Time Varying Delay ◽  
The Stability ◽  
Stochastic Genetic Regulatory Networks ◽  
Delay Dependent

This paper is concerned with the stability problem for a class of uncertain impulsive stochastic genetic regulatory networks (UISGRNs) with time-varying delays both in the leakage term and in the regulator function. By constructing a suitable Lyapunov-Krasovskii functional which uses the information on the lower bound of the delay sufficiently, a delay-dependent stability criterion is derived for the proposed UISGRNs model by using the free-weighting matrices method and convex combination technique. The conditions obtained here are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. In addition, three numerical examples are given to justify the obtained stability results.

scholarly journals Stability Criteria of Interval Time-Varying Delay Systems and Their Application

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Zhanhui Lu ◽  
Chengyong Wang ◽  
Weijuan Wang
Keyword(s):  
Convex Combination ◽  
Combination Method ◽  
Delay Systems ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
The Stability ◽  
Delay Dependent ◽  
Uncertain Linear Systems

The stability for a class of uncertain linear systems with interval time-varying delays is studied. Based on the delay-dividing approach, the delay interval is partitioned into two subintervals. By constructing an appropriate Lyapunov-Krasovskii functional and using the convex combination method and the improved integral inequality, the delay-dependent stability criteria with less conservation are derived. Finally, some numerical examples are given to show the effectiveness and superiority of the proposed method.

scholarly journals Robust filtering for stochastic genetic regulatory networks with time-varying delay

2009 ◽  
Vol 220 (2) ◽  
pp. 73-80 ◽  
Author(s):  
Guoliang Wei ◽  
Zidong Wang ◽  
James Lam ◽  
Karl Fraser ◽  
Ganti Prasada Rao ◽  
...  
Keyword(s):  
Regulatory Networks ◽  
Genetic Regulatory Networks ◽  
Robust Filtering ◽  
Time Varying ◽  
Time Varying Delay ◽  
Stochastic Genetic Regulatory Networks ◽  
Varying Delay

Robust stabilization and H∞ control for discrete-time stochastic genetic regulatory networks with time delays

2012 ◽  
Vol 90 (10) ◽  
pp. 939-953 ◽  
Author(s):  
K. Mathiyalagan ◽  
R. Sakthivel
Keyword(s):  
Discrete Time ◽  
Regulatory Networks ◽  
Robust Stabilization ◽  
Genetic Regulatory Networks ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Stochastic Genetic Regulatory Networks

This paper presents some novel results on robust stabilization and H∞ control design for a class of uncertain discrete-time stochastic genetic regulatory networks (GRNs) with time-varying delays. The GRNs under consideration are subject to stochastic noise, time-varying, and norm bounded parameter uncertainties. By constructing a new Lyapunov–Krasovskii functional that contains some novel triple summation terms, we propose a state feedback gene controller to guarantee that the considered GRN is mean-square asymptotically stable about its equilibrium point for all admissible uncertainties. The other issue is to design a H∞ feedback gene controller so that the GRN is robustly stable with a prescribed H∞ disturbance attenuation level for all admissible uncertainties and for all delays to satisfy both the lower bound and upper bound of the interval time-varying delay. The obtained conditions are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. Finally, the control scheme has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained results.

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.

scholarly journals Exponential Stability Analysis for Genetic Regulatory Networks with Both Time-Varying and Continuous Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lizi Yin ◽  
Yungang Liu
Keyword(s):  
Stability Analysis ◽  
Exponential Stability ◽  
Regulatory Networks ◽  
Convex Combination ◽  
Genetic Regulatory Networks ◽  
Distributed Delays ◽  
Combination Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay

The global exponential stability is investigated for genetic regulatory networks with time-varying delays and continuous distributed delays. By choosing an appropriate Lyapunov-Krasovskii functional, new conditions of delay-dependent stability are obtained in the form of linear matrix inequality (LMI). The lower bound of derivatives of time-varying delay is first taken into account in genetic networks stability analysis, and the main results with less conservatism are established by interactive convex combination method to estimate the upper bound of derivative function of the Lyapunov-Krasovskii functional. In addition, two numerical examples are provided to illustrate the effectiveness of the theoretical results.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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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