Cluster synchronization is of paramount importance for the normal functioning
of numerous technological and natural systems. Deviations from normal cluster
synchronization patterns are closely associated with various malfunctions, such
as neurological disorders in the brain. Therefore, it is crucial to restore
normal system functions by stabilizing the appropriate cluster synchronization
patterns. Most existing studies focus on designing controllers based on state
measurements to achieve system stabilization. However, in many real-world
scenarios, measuring system states, such as neuronal activity in the brain,
poses significant challenges, rendering the stabilization of such systems
difficult. To overcome this challenge, in this paper, we employ an open-loop
control strategy, vibrational control, which does not requires any state
measurements. We establish some sufficient conditions under which vibrational
inputs stabilize cluster synchronization. Further, we provide a tractable
approach to design vibrational control. Finally, numerical experiments are
conducted to demonstrate our theoretical findings.Comment: Submitted to Open Journal of Control System