scholarly journals The Asymptotic Synchronization Analysis for Two Kinds of Complex Dynamical Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Dynamical Networks ◽  
Simulation Results ◽  
Delay Dependent ◽  
Asymptotic Synchronization

We consider a class of complex networks with both delayed and nondelayed coupling. In particular, we consider the situation for both time delay-independent and time delay-dependent complex dynamical networks and obtain sufficient conditions for their asymptotic synchronization by using the Lyapunov-Krasovskii stability theorem and the linear matrix inequality (LMI). We also present some simulation results to support the validity of the theories.

scholarly journals Neural network based asynchronous synchronization for fuzzy hidden Markov jump complex dynamical networks

2021 ◽  
Author(s):  
Chao Ma ◽  
Liziyi Hao ◽  
Hang Fu
Keyword(s):  
Neural Network ◽  
Hidden Markov ◽  
Sufficient Conditions ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Markov Jump ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
The Neural Network ◽  
Takagi Sugeno

AbstractThis paper investigates the drive-response synchronization problem of Takagi–Sugeno fuzzy hidden Markov jump complex dynamical networks. More precisely, a novel asynchronous synchronization control strategy is developed for coping with mismatched hidden jumping modes. Furthermore, the neural network is adopted with online learning laws for unknown function approximation. By taking advantage of Lyapunov method, sufficient conditions are established to ensure mean-square synchronization performance with disturbances. Based on the synchronization criterion, asynchronous controller gains are designed in terms of linear matrix inequalities. An illustrative example is finally given to validate the effectiveness of the proposed synchronization techniques.

scholarly journals Mean-Square Exponential Synchronization of Stochastic Complex Dynamical Networks with Switching Topology by Impulsive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xuefei Wu ◽  
Chen Xu
Keyword(s):  
Impulsive Control ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Complex Dynamical Networks ◽  
Switching Topology ◽  
Linear Matrix ◽  
Mean Square ◽  
Dynamical Networks ◽  
The Mean ◽  
Networks With Switching Topology

This paper investigates the mean-square exponential synchronization issues of delayed stochastic complex dynamical networks with switching topology and impulsive control. By using the Lyapunov functional method, impulsive control theory, and linear matrix inequality (LMI) approaches, some sufficient conditions are derived to guarantee the mean-square exponential synchronization of delay complex dynamical network with switch topology, which are independent of the network size and switch topology. Numerical simulations are given to illustrate the effectiveness of the obtained results in the end.

scholarly journals Synchronization of Chaotic Delayed Neural Networks via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Fang ◽  
Kang Yan ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Impulsive Synchronization ◽  
Synchronization Problem

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

scholarly journals Delay-Dependent Synchronization for Complex Dynamical Networks with Interval Time-Varying and Switched Coupling Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
T. Botmart ◽  
P. Niamsup
Keyword(s):  
Average Dwell Time ◽  
Complex Dynamical Networks ◽  
Delay Systems ◽  
Linear Matrix ◽  
Unitary Matrix ◽  
Fast Time ◽  
Time Varying ◽  
Dynamical Networks ◽  
Interval Time ◽  
Delay Dependent

We investigate the local exponential synchronization for complex dynamical networks with interval time-varying delays in the dynamical nodes and the switched coupling term simultaneously. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. By using common unitary matrix for different subnetworks, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when subnetworks are synchronizable and nonsynchronizable, a delay-dependent sufficient condition is derived and formulated in the form of linear matrix inequalities (LMIs) by average dwell time approach and piecewise Lyapunov-Krasovskii functionals which are constructed based on the descriptor model of the system and the method of decomposition. The new stability condition is less conservative and is more general than some existing results. A numerical example is also given to illustrate the effectiveness of the proposed method.

scholarly journals Delay-Dependent Stability of Uncertain Distributed Time-Delay Systems

2012 ◽  
Vol 6-7 ◽  
pp. 45-48
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Distributed Time Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality (LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

Adaptive Synchronization of Complex Dynamical Networks in Presence of Coupling Connections With Dynamical Behavior

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Ali Kazemy ◽  
Khoshnam Shojaei
Keyword(s):  
Dynamical Behavior ◽  
Adaptive Controller ◽  
Complex Dynamical Networks ◽  
Adaptive Synchronization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Dynamical Networks ◽  
Numerical Examples ◽  
Decision Variables ◽  
Simulation Results

In this paper, the synchronization of complex dynamical networks (CDNs) is investigated, where coupling connections are expressed in terms of state-space equations. As it is shown in simulation results, such links can greatly affect the synchronization and cause synchronization loss, while many real-world networks have these types of connections. With or without time-delay, two different models of the CDNs are presented. Then, by introducing a distributed adaptive controller, the synchronization conditions are derived by utilizing the Lyapunov(–Krasovskii) theorem. These conditions are provided in the form of linear matrix inequalities (LMIs), which can be easily solved by standard LMI solvers even for large networks due to a few numbers of scalar decision variables. At the end, illustrative numerical examples are given to specify the effectiveness of the proposed methods.

scholarly journals RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shengchun Yu ◽  
Guici Chen ◽  
Yi Shen
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay System ◽  
Interval System ◽  
Uncertain Time ◽  
System With Time Delay

The robustH∞control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robustH∞controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robustH∞controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robustH∞controller.

scholarly journals MASTER–SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS WITH TIME-DELAY

2001 ◽  
Vol 11 (06) ◽  
pp. 1707-1722 ◽  
Author(s):  
M. E. YALÇIN ◽  
J. A. K. SUYKENS ◽  
J. VANDEWALLE
Keyword(s):  
Time Delay ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Matrix Inequality ◽  
Lur’E Systems ◽  
Delay Effects ◽  
Feedback Matrix ◽  
Error System ◽  
Delay Dependent ◽  
Synchronization Scheme

In this paper time-delay effects on the master–slave synchronization scheme are investigated. Sufficient conditions for master–slave synchronization of Lur'e systems are presented for a known time-delay in the master and slave systems. A delay-dependent synchronization criterion is given based upon a new Lyapunov–Krasovskii function. The derived criterion is a sufficient condition for global asymptotic stability of the error system, expressed by means of a matrix inequality. The feedback matrix follows from solving a nonlinear optimization problem. The method is illustrated for the synchronization of Chua's circuits, 5-scroll attractors and hyperchaotic attractors.

Robust Stabilization of Uncertain Stochastic Systems with Delay in Control Input

2012 ◽  
Vol 461 ◽  
pp. 40-43 ◽  
Author(s):  
Cheng Wang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequality ◽  
Stochastic Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Control Input ◽  
Matrix Inequality ◽  
Stabilization Condition ◽  
Delay Dependent

This paper discusses the problems of robust stabilization of stochastic systems with parametric uncertainties and time delay in control input. The parametric uncertainties which appear in all system matrices are assumed to be norm bounded. The delay-dependent stabilization condition is derived by taking the relationships between terms in the Leibniz-Newton formula into account. Free-weighting matrices are employed to express these relationship, and the sufficient stabilization condition is formulated in terms of linear matrix inequality (LMI) based on the Lyapunov-Krasovskii theory, which can be solved by LMI toolbox in Matlab

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