Synchronization of stochastic coupled systems via feedback control based on discrete-time state observations

Wu, Yongbao; Chen, Bingdao; Li, Wenxue

doi:10.1016/j.nahs.2017.04.006

Cited by 72 publications

(32 citation statements)

References 41 publications

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“…Remark Notice that if there is a single link (i.e., l = 1), the global Lyapunov function

V (t, e) = \sum_{k = 1}^{n} \prod_{i = 1}^{m} d_{k}^{(i)} V_{k} (t, e_{k})

will become

V false(t, e false) = \sum_{k = 1}^{n} d_{k} V_{k} false(t, e_{k} false)

, where d k denotes the cofactor of the k th diagonal element of Laplacian matrix of digraph

((), scriptG, A)

, which is similar to that in other studies . Thus, our results can seem as a generalization of theirs to some extent.…”

Section: Global Synchronization Analysissupporting

confidence: 62%

“…For the reason that CNs are always large scale, it is relatively difficult to achieve synchronization by themselves, which motivates people to adopt control strategies. Nowadays, lots of effective strategies have been proposed for this issue, such as feedback control, intermittent control, and impulsive control . Considering practice and low cost, people are inclined to discontinuous control, which includes intermittent control and impulsive control, to synchronize CNs.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

2019

Math Methods in App Sciences

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This paper concentrates on the global synchronization of the fractional‐order multi‐linked complex network (FMCN) via periodically intermittent control. It should be stressed that periodically intermittent control is employed to the FMCN for the first time. Moreover, the network is defined on digraphs with different weights, and two situations on topological structure of the network are discussed, including each digraph being strongly connected, and the biggest one being strongly connected. Based on Lyapunov method and graph theory, some synchronization criteria are obtained under two situations. And, the obtained synchronization criteria have a close relationship with the order of fractional‐order derivative, coupling strength, control gain, control rate, and control period. Besides, for practicability, theoretical results are applied to studying the synchronization of fractional‐order multi‐linked chaotic systems, and some sufficient conditions are provided. For a special case, fractional‐order multi‐linked Lorenz chaotic systems, numerical simulations are given to indicate the feasibility of theoretical results and the effectiveness of control strategy.

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“…Remark Notice that if there is a single link (i.e., l = 1), the global Lyapunov function

V (t, e) = \sum_{k = 1}^{n} \prod_{i = 1}^{m} d_{k}^{(i)} V_{k} (t, e_{k})

will become

V false(t, e false) = \sum_{k = 1}^{n} d_{k} V_{k} false(t, e_{k} false)

, where d k denotes the cofactor of the k th diagonal element of Laplacian matrix of digraph

((), scriptG, A)

, which is similar to that in other studies . Thus, our results can seem as a generalization of theirs to some extent.…”

Section: Global Synchronization Analysissupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

2019

Math Methods in App Sciences

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“…Remark In Theorem , we construct the global Lyapunov function as

V false(t false) = \sum_{k = 1}^{n} c_{k} d_{k} V_{k} false(t false)

, where weights c k and d k are the cofactors of the k th diagonal element of

{scriptL}_{\overset{A}{true}}

and

{scriptL}_{\overset{B}{true}}

, respectively, which shows that the exponential stability of the trivial solution of system has a close relationship with the topological structure of the coupled network. This kind of construction was first proposed by Li et al and was applied to many other systems successfully . Theorem extends this construction to CSNs with multicoupling structure.…”

Section: Global Stability Analysismentioning

confidence: 87%

“…Remark In fact, the assumption on the strong connectedness of considered coupled networks is common . If the strong connectedness is not satisfied, only a part of vertices' stability can be promised (see remark 3 in the work of Li et al for a detailed explanation).…”

Section: Global Stability Analysismentioning

confidence: 99%

“…In 2010, Li et al first explored the stability of CSNs by means of the Lyapunov method and graph‐theoretical technique. After that, based on the work of Li and Shuai, many interesting results were reported for more general CSNs, such as the stability of stochastic CSNs, the stability of complex‐valued CSNs, and the synchronization of CSNs . However, it should be pointed out that the aforementioned works only consider CSNs with single coupling.…”

Section: Introductionmentioning

confidence: 99%

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Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Wang

Sun

Fan

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper explores the stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays (ICSNMT). The coupling structure can be nonlinear and the time‐varying delays in which can be different, which can well describe more realistic networks. In order to describe this multicoupling structure, we build ICSNMT on a digraph with multiple arcs. Two cases are discussed, ie, (i) the continuous dynamics is stable and (ii) the impulsive dynamics is stable. Then, by means of impulsive differential inequalities with multiple delays and weighted Lyapunov functions method where the weights are closely linked to the network's topological structure, some stability criteria are established. Then, the theoretical results are illustrated by examples of bidirectional associative memory neural networks and coupled modified Chua's circuits, respectively. The numerical simulations are also carried out to demonstrate the effectiveness and feasibility of our theoretical findings.

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Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

Liu

2018

Asian Journal of Control

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In this paper, finite-time stabilization of coupled systems on networks with time-varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self-delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite-time stabilization of coupled oscillators with time-varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.

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Synchronization of stochastic coupled systems via feedback control based on discrete-time state observations

Cited by 72 publications

References 41 publications

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

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