scholarly journals Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 405 ◽  
Author(s):  
Xudong Hai ◽  
Guojian Ren ◽  
Yongguang Yu ◽  
Conghui Xu
Keyword(s):  
Complex Networks ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Communication Topology ◽  
General Network ◽  
Inequality Techniques ◽  
Adaptive Control Strategy ◽  
Pinning Scheme

In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

Dynamical Behaviors of Stochastic Hopfield Neural Networks with Reaction-Diffusion Terms

2013 ◽  
Vol 432 ◽  
pp. 523-527
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Hopfield Neural Network ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Diffusion Effects ◽  
Weak Attractor ◽  
Theoretical Results

Dynamical behaviors of stochastic Hopfield neural network with delays and reaction-diffusion terms are investigated. By employing Lyapunov method, Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness, weak attractor and asymptotic stability are obtained. The criteria are independent of the magnitude of the delays, and dependent on the diffusion effects and the derivative of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

scholarly journals Limited-Budget Formation Control for High-Order Linear Swarm Systems with Fix Topologies

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hongtao Dang ◽  
Le Wang ◽  
Yan Zhang ◽  
Jianye Yang
Keyword(s):  
Formation Control ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
High Order ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Order Linear ◽  
Limited Budget ◽  
Communication Topology ◽  
Formation Design

This paper discusses limited-budget time-varying formation design and analysis problems for a high-order linear swarm system with a fixed communication topology. Firstly, the communication topology among agents is modeled as an undirected and connected graph, and a new formation control protocol with an energy integral term is proposed to realize formation control and to guarantee the practical energy assumption is less than the limited energy budget. Then, by the matrix inequality tool, sufficient conditions for limited-budget formation design and analysis are proposed, respectively, which are scalable and checkable since they are independent of the number of agents of a swarm system and can be transformed into linear matrix inequality constraints. Moreover, an explicit expression of the formation center function is given, which contains the formation function part and the cooperative state part and is not associated with the derivatives of the formation functions. Finally, a numerical simulation is shown to demonstrate the effectiveness of theoretical results.

Unfragile Passive Control of Uncertain Sampling System

2013 ◽  
Vol 325-326 ◽  
pp. 1170-1175
Author(s):  
Qing Zhi Liu
Keyword(s):  
Control Problem ◽  
Robust Stability ◽  
Passive Control ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Sampling System ◽  
State Delay ◽  
Index Terms

The unfragile passive control problem of a class of uncertain state-delay sampling system is discussed. Applying Lyapunov method, and combining the properties of matrix inequality, the sufficient condition of robust stability is given, and the unfragile passive controller is designed. Finally a numerical example illustrates the effectiveness and the availability for the design.Index Terms - Uncertain State-delay Sampling System , Linear Matrix Inequility , Unfragile Passive Control .

Robust projective outer synchronization of coupled uncertain fractional-order complex networks

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Junwei Wang ◽  
Yun Zhang
Keyword(s):  
Complex Networks ◽  
Fractional Order ◽  
Small World ◽  
Linear Matrix ◽  
Control Law ◽  
Order Complex ◽  
Outer Synchronization ◽  
World Communication ◽  
Special Cases ◽  
Communication Topology

AbstractIn this work, we propose a novel projective outer synchronization (POS) between unidirectionally coupled uncertain fractional-order complex networks through scalar transmitted signals. Based on the state observer theory, a control law is designed and some criteria are given in terms of linear matrix inequalities which guarantee global robust POS between such networks. Interestingly, in the POS regime, we show that different choices of scaling factor give rise to different outer synchrony, with various special cases including complete outer synchrony, anti-outer synchrony and even a state of amplitude death. Furthermore, it is demonstrated that although stability of POS is irrelevant to the inner-coupling strength, it will affect the convergence speed of POS. In particular, stronger inner synchronization can induce faster POS. The effectiveness of our method is revealed by numerical simulations on fractional-order complex networks with small-world communication topology.

Dynamical Behaviors of Stochastic Reaction-Diffusion Hopfield Neural Networks

2013 ◽  
Vol 787 ◽  
pp. 921-925
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Diffusion Effects ◽  
Stochastic Reaction ◽  
Theoretical Results

Dynamical behaviors of stochastic reaction-diffusion Hopfield neural networks with delays are investigated. By employing Lyapunov method, Hardy-Poincare inequality and linear matrix inequality, some novel criteria on ultimate boundedness and asymptotic stability are obtained. The sufficient criteria depend on the diffusion effects and are independent of the magnitude of the delays. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

scholarly journals Global Synchronization of Complex Networks with Discrete Time Delays on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Quanxin Cheng ◽  
Jinde Cao
Keyword(s):  
Complex Networks ◽  
Time Scales ◽  
Discrete Time ◽  
Time Delays ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Global Synchronization ◽  
Synchronization Problem

This paper studies the global synchronization problem for a class of complex networks with discrete time delays. By using the theory of calculus on time scales, the properties of Kronecker product, and Lyapunov method, some sufficient conditions are obtained to ensure the global synchronization of the complex networks with delays on time scales. These sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). The main contribution of the result is that the global synchronization problems with both discrete time and continuous time are unified under the same framework.

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