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In this article, motivated by a recent work of R. Brockett , 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 conditionsdoi:10.1109/tcns.2018.2813927 fatcat:nofthb7tjjcybbn3c5seekquce