Robust Global Synchronization of Brockett Oscillators

In this paper, motivated by a recent work “Synchronization without periodicity (2013),” a robust global synchronization problem of multistable Brockett oscillators has been studied within an input-to-state stability framework. 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 nonidentical oscillators in contrast to the local analysis presented in “Mathematical Systems Theory, A Volume in Honor of U. Helmke.” Numerical simulation examples illustrate our theoretical results.