Master–slave Synchronization of Lur'e Systems With Time-Delay

Yalçın, Müştak E.; Suykens, Johan A. K.; Vandewalle, Joos

doi:10.1142/s021812740100295x

Cited by 219 publications

(156 citation statements)

References 30 publications

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“…21 This Lyapunov-Krasovskii functional is more general than the more "classical" LyapunovKrasovskii functionals employed in other work. 10,17 As a consequence of this greater generality, the result of Theorem 1 is less conservative than results that would have been obtained using the more classical functionals.…”

Section: Remarkmentioning

confidence: 94%

“…Pyragas 9 considered the synchronization of two directionally coupled Mackey-Glass systems. Yalçin et al 10 discussed the ͑nonan-ticipative͒ master-slave synchronization of time-delayed Lur'e systems, and the results obtained were later generalized. 11,12 Senthilkumar and Lakshmanan 13 discussed the transitions from anticipating synchronization to lag synchronization via complete synchronization of time-delay systems with two time delays.…”

Section: Introductionmentioning

confidence: 99%

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Anticipating synchronization of chaotic Lur’e systems

Huijberts

Nijmeijer

Oguchi

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper we consider the anticipating synchronization of chaotic time-delayed Lur'e-type systems in a master-slave setting. We introduce three scenarios for anticipating synchronization, and give sufficient conditions for the existence of anticipating synchronizing slave systems in terms of linear matrix inequalities. The results obtained are illustrated on a time-delayed Rössler system and a time-delayed Chua oscillator. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2710964͔In their ground breaking 1990 paper, Pecora and Carroll 1 showed that, in spite of sensitive dependence on initial conditions, coupled chaotic systems can synchronize. Following this work, in the last decades considerable interest in the notion of synchronization of complex or chaotic systems has arisen. Among others, perhaps the main motivation so far seems to lie in potential applications regarding secure or private communications, though the number of reported applications is still limited to date. On the other hand synchronization appears in numerous different ways, most notably in biological applications (heart beat, brain activity, neural activity, walking, etc.), nature (planetary motion), physics (organ pipes, etc.) and engineering (coordinated robot motion, etc.). 2-4 More recently, it was observed by Voss 5 that coupled chaotic Ikeda time-delay systems can exhibit what is called anticipating synchronization in that the state of one of the systems synchronizes with the future state of the other system, which allows one to predict the state of the latter system in spite of the inherent unpredictability of chaotic systems. In many applications where synchronization seems to be essential, the coupling between systems naturally contains a small amount of delay that nevertheless does not prevent synchronization from occurring. In this regard one may think about transport delay (e.g., chemical transport between cells in a living organism) or other forms of delay like optical delay in the synchronized movement of swarms of birds. Another example occurs when multiple agents, like, e.g., robots, share a communication network, which in principle will lead to a natural delay in the execution of (shared) tasks. It is therefore of interest to investigate how anticipating synchronization can be achieved for general classes of complex or chaotic systems. In this paper we will consider a wide class of chaotic time-delay systems, so-called Lur'e systems, and discuss when and how one can design anticipating synchronization schemes for these systems.

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Section: Remarkmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Anticipating synchronization of chaotic Lur’e systems

Huijberts

Nijmeijer

Oguchi

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Section: Introductionmentioning

confidence: 99%

“…Guo and Zhong in [6] and Yalcin et al in [21] derived some delay-independent [9] and delay-dependent synchronization criteria for global asymptotic stability of the error system, which are expressed as LMIs and derived from extended LKFs. Liao and Chen [11] and Cao et al [1] further generalized and improved the results in [21] and employed model transformation, which leads to some conservative synchronization criteria for inducing additional terms. Shortly, some new approaches are employed to avoid using model transformation and derive much less conservative synchronization conditions, for example, Xiang et al [20], He et al [8] used integral inequality [22] in the derivative of Lyapunov functional respectively, and it turned out that the permissible delay threshold can be fairly enlarged both in theory and in numerical experiment.…”

Section: Introductionmentioning

confidence: 99%

New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

Wang¹,

Xiong²,

Liu³

et al. 2017

J. Nonlinear Sci. Appl.

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This paper studies the problem of master-slave synchronization for uncertain Lur'e system via time-varying delayed feedback control. It proves a new inequality involving double integrals, which can reduce the conservatism of the known Jensen's like inequalities according to our analysis. By employing this new inequality and a new class of novel mode-dependent augmented Lyapunov-Krasovskii functional (LKF), it establishes some novel synchronization criteria, where the controller gain can be achieved by solving a set of linear matrix inequalities (LMIs). Two examples with numerical simulations are given to illustrate the feasibility and the superiority of our methods.

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“…This type of coupling has been widely used to investigate synchronization problems in various fields such as electric circuit [53,54], coupled pendulums [55], delayed neural networks (DNNS) [56], and general models [57][58][59][60][61][62][63]. In a recent paper, we have showed that the former type of delayed coupling can enhance spatiotemporal order in coupled neuronal systems [40].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

Jiang

Hou

2011

Chaos, Solitons & Fractals

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We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling:For the former case, we show that time delay in the coupling can dramatically enhance temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time τ is tuned to nearly match the intrinsic spike period of the neuronal network, the system dynamics reaches a most ordered state, which is both periodic in time and nearly synchronized in space, demonstrating an interesting resonance phenomenon with delay. For the latter case, however, we can not achieve a similar spatiotemporal ordered state, but the neuronal dynamics exhibits interesting synchronization transition with time delay from zigzag fronts of excitations to dynamic clustering anti-phase synchronization (APS), and further to clustered chimera states which have spatially distributed anti-phase coherence separated by incoherence. Furthermore, we also show how these findings are influenced by the change of the noise intensity and the rewiring probability. Finally, qualitative analysis is given to illustrate the numerical results. * Electronic address: hzhlj@ustc.edu.cn

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Master–slave Synchronization of Lur'e Systems With Time-Delay

Cited by 219 publications

References 30 publications

Anticipating synchronization of chaotic Lur’e systems

Anticipating synchronization of chaotic Lur’e systems

New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

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