In this article, motivated by a recent work of R. Brockett [1], 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

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... r. The conditions obtained in our work are global and applicable to families of non-identical oscillators in contrast to the local analysis of [1]. Numerical simulation examples illustrate our theoretical results.