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 Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

A DELAY-DEPENDENT APPROACH TO ROBUST TAKAGI–SUGENO FUZZY CONTROL OF UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2011 ◽  
Vol 20 (08) ◽  
pp. 1571-1589 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Fuzzy Control ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper deals with the problem of globally delay-dependent robust stabilization for Takagi–Sugeno (T–S) fuzzy neural network with time delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Based on Lyapunov–Krasovskii functional approach and linear matrix inequality technique, delay-dependent sufficient conditions are derived for ensuring the exponential stability for the closed-loop fuzzy control system. An important feature of the result is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using the proposed techniques for achieving delay dependence. Another feature of the results lies in that involves fewer matrix variables. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design methods.

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 analysis of uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties via augmented Lyapunov functional

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1179-1188
Author(s):  
R. Jeetendra ◽  
Vernold Vivin
Keyword(s):  
Lyapunov Functional ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Lower And Upper Bounds ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Nonlinear Uncertainties ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this work, the problem of delay-dependent stability for uncertain stochastic systems with interval time-varying delays and nonlinear uncertainties is addressed. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing an augmented Lyapunov functional, a new delay interval-dependent stability criterion for the system is obtained in terms of Linear Matrix Inequalities (LMIs). Comparisons are made through numerical examples and less conservatism results are reported.

scholarly journals Robust Stability and Stabilization of a Class of Uncertain Nonlinear Discrete-Time Stochastic Systems with Interval Time-Varying Delays

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shuang Liang ◽  
Yali Dong
Keyword(s):  
Discrete Time ◽  
Stochastic Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Stochastic Stabilization ◽  
Stability And Stabilization ◽  
Delay Dependent

This paper deals with the problems of the robust stochastic stability and stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays and nonlinear disturbances. By utilizing a new Lyapunov-Krasovskii functional and some well-known inequalities, some new delay-dependent criteria are developed to guarantee the robust stochastic stability of a class of uncertain discrete-time stochastic systems in terms of the linear matrix inequality (LMI). Then based on the state feedback controller, the delay-dependent sufficient conditions of robust stochastic stabilization for a class of uncertain discrete-time stochastic systems with interval time-varying delays are established. The controller gain is designed to ensure the robust stochastic stability of the closed-loop system. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed method.

A DELAY-DEPENDENT APPROACH TO ROBUST PASSIVITY ANALYSIS FOR TAKAGI-SUGENO FUZZY UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2013 ◽  
Vol 21 (03) ◽  
pp. 415-433 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Passivity Analysis ◽  
Fuzzy Neural ◽  
Delay Dependent

This paper deals with the passivity analysis problem for Takagu-Sugeno (T-S) fuzzy neural networks with mixed interval time-varying delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Delay-dependent sufficient conditions for the passivity problem are obtained by using Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique. The important feature of the results lies in that it does not make use of upper bounds to introduce some degree of conservativeness. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design procedures.

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.

scholarly journals Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Leakage Term ◽  
Interval Time ◽  
Robust Synchronization ◽  
Delay Dependent ◽  
Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals New Delay-Dependent Robust Stability Criterion for LPD Discrete-Time Systems with Interval Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Narongsak Yotha ◽  
Kanit Mukdasai
Keyword(s):  
Robust Stability ◽  
Discrete Time ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Discrete Time Systems ◽  
Delay Dependent ◽  
Parameter Dependent ◽  
Time Systems

This paper investigates the problem of robust stability for linear parameter-dependent (LPD) discrete-time systems with interval time-varying delays. Based on the combination of model transformation, utilization of zero equation, and parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent robust stability conditions are obtained and formulated in terms of linear matrix inequalities (LMIs). Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

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