Synchronization for time-varying complex dynamical networks with different-dimensional nodes and non-dissipative coupling

Zhang, Lili; Wang, Yinhe; Wang, Qingyun

doi:10.1016/j.cnsns.2014.12.012

Cited by 22 publications

(18 citation statements)

References 28 publications

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“…Unfortunately, this assumption is not always the case for realistic networks. In fact, just as was pointed out in , many realistic networks are composed of different‐dimensional nodes. Compared with the networks consisting of the same‐dimensional nodes, the networks with different‐dimensional nodes will exhibit more complex properties and their stabilization is more challenging.…”

Section: Introductionmentioning

confidence: 83%

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Stabilization of Time‐Varying and Disturbed Complex Dynamical Networks with Different‐Dimensional Nodes and Uncertain Nonlinearities

Zhang

Lei

Wang

et al. 2017

Asian Journal of Control

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This paper investigates the stabilization problem for time-varying and disturbed complex dynamical networks (CDNs) with different-dimensional nodes and uncertain nonlinearities. To be consistent with the properties of real-world networks, both the disturbances of our networks and the nonlinear structures of the nodes permit are completely unknown but bounded. Furthermore, the norm bounds of the uncertain nonlinearities and disturbances (NBUND) are applied to design the stabilization controllers. When the NBUND are known in advance, some decentralized state feedback controllers are proposed to stabilize our networks. And when they are unknown, adaptive decentralized stabilization schemes are brought forward for our network models. The effectiveness and feasibility of our theoretical results are verified by two simulation examples.

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Section: Introductionmentioning

confidence: 83%

“…In particular many studies have focused on such typical collective behaviors as stability and synchrony of CDNs. Till now, many fruitful research avenues have been pursued in and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of Time‐Varying and Disturbed Complex Dynamical Networks with Different‐Dimensional Nodes and Uncertain Nonlinearities

Zhang

Lei

Wang

et al. 2017

Asian Journal of Control

Self Cite

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“…The Jacobian matrix of ( ( )) at ( ) is ( ); then the synchronized states (2) are the same as the asymptotically stable results of system (9).…”

Section: Assumption 1 the Outer-coupling Matric Satisfiesmentioning

confidence: 99%

“…Then more matrix-valued coefficients can be introduced to reduce conservatism. Moreover, our methods can also be applied to most of the existing synchronization results, such as [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Remark 9 Convergent Lmi Relaxations Are Introduced Bymentioning

confidence: 99%

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Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

et al. 2017

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The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler's Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov's stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.

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Matrix projective cluster synchronization for arbitrarily coupled networks with different dimensional nodes via nonlinear control

Zhang

Wang

et al. 2019

Intl J Robust & Nonlinear

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Recently, many control mechanisms have been put forward to realize the cluster synchronization of networks. However, these results are derived by making very conservative assumptions on the network's nodes and its outer coupling configuration matrix, which greatly limit these results' potential applications. This paper focuses on weakening these restrictive assumptions as much as possible and further proposes nonlinear controllers for our general networks to achieve matrix projective cluster synchronization (MPCS). One outstanding characteristic of our introduced network model is that the state dimensions of the nodes in different clusters are different, which extends the case that the network is composed of identical dimensional nodes. Another distinctive characteristic is that no other restrictions are imposed on our network's outer coupling matrix except for being bounded, namely, both the outer coupling matrix and its block matrices may be time varying and nonzero-row-sum. Besides, the exponential MPCS (EMPCS) and asymptotic MPCS (AMPCS) are defined to make a better description of the cluster synchronization phenomena in this paper. It is worth noted that these two definitions extend the existing ones about cluster synchronization. Furthermore, by means of rigorous theoretical analysis, some nonlinear control strategies are proposed for our network to realize EMPCS or AMPCS. At last, a proper numerical example along with two control patterns is presented to demonstrate the validity and effectivity of our results in this paper. KEYWORDSarbitrarily coupled, complex dynamical networks (CDNs), different dimensional nodes, matrix projective cluster synchronization (MPCS), nonlinear control strategies INTRODUCTIONCurrently, a very high level of concern among researchers from a variety of engineering and science fields has been given to complex dynamical networks (CDNs) due to their ubiquity and widespread applications. Synchronization, which is a significant and interesting collective behavior of networks, not only can explicate lots of natural phenomena but also has numerous potential applications in many fields such as laser transmission, information science, and secure communication. 1-8 Therefore, for the synchronization of networks, a lot of investigations have been done from various 3650

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Synchronization for time-varying complex dynamical networks with different-dimensional nodes and non-dissipative coupling

Cited by 22 publications

References 28 publications

Stabilization of Time‐Varying and Disturbed Complex Dynamical Networks with Different‐Dimensional Nodes and Uncertain Nonlinearities

Stabilization of Time‐Varying and Disturbed Complex Dynamical Networks with Different‐Dimensional Nodes and Uncertain Nonlinearities

Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

Matrix projective cluster synchronization for arbitrarily coupled networks with different dimensional nodes via nonlinear control

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