scholarly journals H∞-Based Pinning Synchronization of General Complex Dynamical Networks with Coupling Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bowen Du ◽  
Dianfu Ma
Keyword(s):  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
External Disturbances ◽  
Dynamical Networks ◽  
Attenuation Index ◽  
General Complex ◽  
Local Feedback ◽  
Theoretical Results

This paper investigates the synchronization of complex dynamical networks with coupling delays and external disturbances by applying local feedback injections to a small fraction of nodes in the whole network. Based onH∞control theory, some delay-independent and -dependent synchronization criteria with a prescribedH∞disturbances attenuation index are derived for such controlled networks in terms of linear matrix inequalities (LMIs), which guarantee that by placing a small number of feedback controllers on some nodes, the whole network can be pinned to reach network synchronization. A simulation example is included to validate the theoretical results.

STABILITY OF TWO TYPICAL COMPLEX DYNAMICAL NETWORKS

2008 ◽  
Vol 22 (05) ◽  
pp. 553-560 ◽  
Author(s):  
WU-JIE YUAN ◽  
XIAO-SHU LUO ◽  
PIN-QUN JIANG ◽  
BING-HONG WANG ◽  
JIN-QING FANG
Keyword(s):  
Numerical Simulation ◽  
Dissipative System ◽  
Small World ◽  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
General Complex ◽  
The Stability ◽  
Theoretical Results

When being constructed, complex dynamical networks can lose stability in the sense of Lyapunov (i. s. L.) due to positive feedback. Thus, there is much important worthiness in the theory and applications of complex dynamical networks to study the stability. In this paper, according to dissipative system criteria, we give the stability condition in general complex dynamical networks, especially, in NW small-world and BA scale-free networks. The results of theoretical analysis and numerical simulation show that the stability i. s. L. depends on the maximal connectivity of the network. Finally, we show a numerical example to verify our theoretical results.

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 Semiglobal Finite-Time Synchronization of Complex Dynamical Networks via Periodically Intermittent Control

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yihan Fan ◽  
Hongmei Liu ◽  
Jun Mei
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Dynamical Networks ◽  
Periodically Intermittent Control ◽  
Finite Time Stability ◽  
Synchronization Problem ◽  
Theoretical Results

This paper studies the finite-time synchronization problem for a class of complex dynamical networks by means of periodically intermittent control. Based on some analysis techniques and finite-time stability theory, some novel and effective finite-time synchronization criteria are given in terms of a set of linear matrix inequalities. Particularly, the previous synchronization problem by using periodically intermittent control has been extended in this paper. Finally, numerical simulations are presented to verify the theoretical results.

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 Intermittent Time-Varying Formation Control for High-Order Networked Agents Subject to Discontinuous Communications

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Lixin Wang ◽  
Zhe Luo ◽  
Xiaoqiang Li ◽  
Xinsan Li ◽  
Xiaogang Yang
Keyword(s):  
Formation Control ◽  
Linear Matrix ◽  
Control Input ◽  
Intermittent Control ◽  
Movement Trajectory ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Communication Time ◽  
Theoretical Results ◽  
Formation Design

This paper investigates the leaderless and leader-follower time-varying formation design and analysis problems for a group of networked agents subject to discontinuous communications. Firstly, a leaderless time-varying formation control protocol is proposed via the intermittent control strategy, where the control input of each agent is constructed by the distributed local state information and formation instructions in the communication time unit, but it is zero in the noncommunication time unit. Then, an explicit formulation of the formation center function is determined to describe the formation movement trajectory of the whole networked agents. Leaderless time-varying formation design and analysis with discontinuous communications are given in the form of linear matrix inequalities. Moreover, the main results of the leaderless cases are extended to the leader-follower cases. Finally, two numerical examples are provided to illustrate the theoretical results of leaderless and leader-follower cases, respectively.

scholarly journals Exponential Synchronization for Neutral Complex Dynamical Networks with Interval Mode-Dependent Delays and Sampled Data

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Xinghua Liu ◽  
Hongsheng Xi
Keyword(s):  
Exponential Stability ◽  
Exponential Synchronization ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Sampled Data ◽  
Neutral Complex ◽  
Dynamical Networks ◽  
Markovian Jump Parameters

The exponential synchronization and sampled-data controller problem for a class of neutral complex dynamical networks (NCDNs) with Markovian jump parameters, partially unknown transition rates and delays, is investigated in this paper. Both the discrete and neutral delays are considered to be interval mode dependent and time varying, while the sampling period is assumed to be time varying and bounded. Based on a new augmented stochastic Lyapunov functional, the delay-range-dependent and rate-dependent exponential stability conditions for the closed-loop error system are obtained by the Lyapunov-Krasovskii stability theory and reciprocally convex lemma. Then according to the proposed exponential stability conditions, the sampled-data synchronization controllers are designed in terms of the solution to linear matrix inequalities that can be solved effectively by using Matlab. Finally, numerical examples are given to demonstrate the feasibility and effectiveness of the proposed methods.

Synchronization and Bifurcation of General Complex Dynamical Networks

2007 ◽  
Vol 47 (6) ◽  
pp. 1073-1075 ◽  
Author(s):  
Sun Wei-Gang ◽  
Xu Cong-Xiang ◽  
Li Chang-Pin ◽  
Fang Jin-Qing
Keyword(s):  
Complex Dynamical Networks ◽  
Dynamical Networks ◽  
General Complex

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.

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