Robust global synchronization of Brockett oscillators

Hafiz Ahmed 1 Rosane Ushirobira 2 Denis Efimov 2, 3
2 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this article, motivated by a recent work of R. Brockett [Brockett, 2013], a robust global synchronization problem of multistable Brockett oscillators has been studied within an Input-to-State Stability (ISS) framework. Following a recent generalization of the classical ISS theory to multistable systems and its application to the synchronization of multistable systems, two synchronization protocols are designed with respect to compact invariant sets of the unperturbed Brockett oscillator. The conditions obtained in our work are global and applicable to families of non-identical oscillators in contrast to the local analysis of [Brockett, 2013]. Numerical simulation examples illustrate our theoretical results.
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Hafiz Ahmed, Rosane Ushirobira, Denis Efimov. Robust global synchronization of Brockett oscillators. [Research Report] Inria Lille - Nord Europe. 2017. ⟨hal-01391120v2⟩

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