scholarly journals Stability analysis of genetic regulatory networks via a linear parameterization approach

2021 ◽  
Author(s):  
Shasha Xiao ◽  
Zhanshan Wang
Keyword(s):  
Regulatory Networks ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Genetic Regulatory Networks ◽  
Mean Value Theorem ◽  
Linear Matrix ◽  
Combination Technique ◽  
Parameterization Method ◽  
Linear Parameterization

AbstractThis paper investigates the problem of finite-time stability (FTS) for a class of delayed genetic regulatory networks with reaction-diffusion terms. In order to fully utilize the system information, a linear parameterization method is proposed. Firstly, by applying the Lagrange’s mean-value theorem, the linear parameterization method is applied to transform the nonlinear system into a linear one with time-varying bounded uncertain terms. Secondly, a new generalized convex combination lemma is proposed to dispose the relationship of bounded uncertainties with respect to their boundaries. Thirdly, sufficient conditions are established to ensure the FTS by resorting to Lyapunov Krasovskii theory, convex combination technique, Jensen’s inequality, linear matrix inequality, etc. Finally, the simulation verifications indicate the validity of the theoretical results.

Robust Finite-Time Passivity for Discrete-Time Genetic Regulatory Networks with Markovian Jumping Parameters

2016 ◽  
Vol 71 (4) ◽  
pp. 289-304 ◽  
Author(s):  
R. Sakthivel ◽  
M. Sathishkumar ◽  
B. Kaviarasan ◽  
S. Marshal Anthoni
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Time Interval ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping

AbstractThis article addresses the issue of robust finite-time passivity for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time-varying delays and Markovian jumping parameters. By constructing a proper Lyapunov–Krasovskii functional involving the lower and upper bounds of time delays, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantees the finite-time boundedness and finite-time passivity of the addressed GRNs for all admissible uncertainties and satisfies the given passive performance index. More precisely, the conditions are obtained with respect to the finite-time interval, while the exogenous disturbances are unknown but energy bounded. Furthermore, the Schur complement together with reciprocally convex optimisation approach is used to simplify the derivation in the main results. Finally, three numerical examples are provided to illustrate the validity 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 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 Improved Delay-Dependent Stability Criterion for Genetic Regulatory Networks with Interval Time-Varying Delays via New Lyapunov Functionals

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
Aphirak Boonpikum ◽  
Thongchai Botmart ◽  
Piyapong Niamsup ◽  
Wajaree Weera
Keyword(s):  
Lyapunov Functional ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Multiple Integral ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent

In this work, the stability analysis problem of the genetic regulatory networks (GRNs) with interval time-varying delays is presented. In the previous works, the constructions of Lyapunov functional have usually been in simple Lyapunov functional, augmented Lyapunov functional, and multiple integral Lyapunov functional. Therefore, we introduce new Lyapunov functionals expressed in terms of delay product functions. New delay-dependent sufficient conditions for the genetic regulatory networks (GRNs) are established in the terms of linear matrix inequalities (LMIS). In addition, a numerical example is provided to illustrate the effectiveness of the theoretical results.

scholarly journals Finite-Time Stability Analysis of Switched Genetic Regulatory Networks with Time-Varying Delays via Wirtinger’s Integral Inequality

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Shanmugam Saravanan ◽  
M. Syed Ali ◽  
Grienggrai Rajchakit ◽  
Bussakorn Hammachukiattikul ◽  
Bandana Priya ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Finite Time ◽  
Regulatory Networks ◽  
Convex Combination ◽  
Genetic Regulatory Networks ◽  
Linear Matrix ◽  
Dynamical Characteristic ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability

The problem of finite-time stability of switched genetic regulatory networks (GRNs) with time-varying delays via Wirtinger’s integral inequality is addressed in this study. A novel Lyapunov–Krasovskii functional is proposed to capture the dynamical characteristic of GRNs. Using Wirtinger’s integral inequality, reciprocally convex combination technique and the average dwell time method conditions in the form of linear matrix inequalities (LMIs) are established for finite-time stability of switched GRNs. The applicability of the developed finite-time stability conditions is validated by numerical results.

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 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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