• system stabilization
• network systems
• vibrational control
• deep brain stimulation

Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on stabilization assume that network systems' states can be measured online so that feedback control strategies can be used. However, in many real-world scenarios, systems' states, e.g., neuronal activity in the brain, are often difficult to measure. In this thesis, we take this situation into account and study the stabilization problem of linear network systems with an open-loop control strategy: vibrational control. We derive a graph-theoretic sufficient condition for structural vibrational stabilizability, under which network systems can always be stabilized. We further provide an approach to select the locations in the network for control placement and design corresponding vibrational inputs to stabilize systems that satisfy this condition. Moreover, we extend some already existing results about theory of classical vibrational control, giving a new formula to predict the effects of this control technique. Finally, we provide some numerical results that demonstrate the validity of our theoretical findings.