Contraction Theory and Master Stability Function: Linking Two Approaches to Study Synchronization of Complex Networks

Russo, Giovanni; Bernardo, Mario di

doi:10.1109/tcsii.2008.2011611

Cited by 91 publications

(50 citation statements)

References 30 publications

(43 reference statements)

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“…Some of the proposed synchronization conditions for complex phase oscillator networks can be evaluated only numerically since they are state-dependent Kumagai, 1980, 1982) or arise from a non-trivial linearization process of full state space oscillator models. The latter procedure is adopted in the widely-studied Master Stability Function formalism, see (Pecora and Carroll, 1998;Boccaletti et al, 2006;Arenas et al, 2008) for the original reference and relevant surveys, see (Restrepo et al, 2004;Sun et al, 2009;Sorrentino and Porfiri, 2011) for its extension to quasi-identical oscillators, and see (Shafi et al, 2013;Russo and Di Bernardo, 2009) for related linearizationbased approaches from the control community.…”

Section: Survey Of Synchronization Metrics and Conditionsmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.

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Section: Survey Of Synchronization Metrics and Conditionsmentioning

confidence: 99%

Synchronization in complex networks of phase oscillators: A survey

2014

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“…Note that many chaotic and hyperchaotic systems such as jerk family system, two-cell quantum-CNN, and modified Bloch equations with feedback field could be described by system (14). Expression (14) is an interesting form because it describes the whole complex chaotic system and makes its dynamics behavior analysis easy such as stability and bifurcations.…”

Section: Model Descriptionmentioning

confidence: 99%

“…Synchronization techniques have been improved in recent years, and many different methods are applied theoretically and experimentally to synchronize the chaotic systems which include back stepping design technique [4], projective synchronization (PS) [5], modified projective synchronization (MPS) [6,7], generalized synchronization [8], adaptive modified projective synchronization [9], lag synchronization [10], anticipating synchronization [11], phase synchronization [12], and their combinations [13]. Synchronization may involve several systems without a prescribed hierarchy (bidirectional) as it is the case in synchronization of networks of systems [14,15], often happening naturally, for instance, in certain biological systems. Another intensive area of research to emphasize within bidirectional synchronization is the study of the consensus paradigm (see an excellent text in [16]).…”

Section: Introductionmentioning

confidence: 99%

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

Kammogne

Fotsin

2014

Journal of Chaos

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A method of estimation of all parameters of a class of nonlinear uncertain dynamical systems is considered, based on the modified projective synchronization (MPS). The case of modified Colpitts oscillators is investigated. Through a suitable transformation of the dynamical system, sufficient conditions for achieving synchronization are derived based on Lyapunov stability theory. Global stability and asymptotic robust synchronization of the considered system are investigated. The proposed approach offers a systematic design procedure for robust adaptive synchronization of a large class of chaotic systems. The combined effect of both an additive white Gaussian noise (AWGN) and an artificial perturbation is numerically investigated. Results of numerical simulations confirm the effectiveness of the proposed control strategy.

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“…Examples include intrinsic observer design [AR03], consensus problems in complex networks [WS05], output regulation of nonlinear systems [PvdWN05], design of frequency estimators [SK08b], synchronization of coupled identical dynamical systems [RdBS09], construction of symbolic models for nonlinear control systems [PGT08,PT09,GPT09], and the analysis of bio-molecular systems [RdB09]. Our motivation comes from symbolic control where incremental stability was identified as a key property enabling the construction of finite abstractions of nonlinear control systems [PGT08,PT09,GPT09,ZPJT10].…”

Section: Introductionmentioning

confidence: 99%

Backstepping Design for Incremental Stability

Zamani

Tabuada

2011

IEEE Trans. Automat. Contr.

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Abstract. Stability is arguably one of the core concepts upon which our understanding of dynamical and control systems has been built. The related notion of incremental stability, however, has received much less attention until recently, when it was successfully used as a tool for the analysis and design of intrinsic observers, output regulation of nonlinear systems, frequency estimators, synchronization of coupled identical dynamical systems, symbolic models for nonlinear control systems, and bio-molecular systems. However, most of the existing controller design techniques provide controllers enforcing stability rather than incremental stability. Hence, there is a growing need to extend existing methods or develop new ones for the purpose of designing incrementally stabilizing controllers. In this paper, we develop a backstepping design approach for incremental stability. The effectiveness of the proposed method is illustrated by synthesizing a controller rendering a synchronous generator incrementally stable.

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Contraction Theory and Master Stability Function: Linking Two Approaches to Study Synchronization of Complex Networks

Cited by 91 publications

References 30 publications

Synchronization in complex networks of phase oscillators: A survey

Synchronization in complex networks of phase oscillators: A survey

Adaptive Control for Modified Projective Synchronization-Based Approach for Estimating All Parameters of a Class of Uncertain Systems: Case of Modified Colpitts Oscillators

Backstepping Design for Incremental Stability

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