This paper deals with a robust synchronization problem for multistable systems evolving on manifolds in the context of Input-to-State Stability (ISS) framework. Based on a recent generalization of classical ISS theory to multistable systems (may have unstable equilibrium), a robust synchronization protocol is designed with respect to a compact invariant set of the unperturbed system. The invariant set is assumed to admit a decomposition without cycles (basically no homoclinic nor heteroclinic orbits may exist). Numerical simulation examples illustrate our theoretical results.