Communication systems are required to transmit wide area measurements which could be used to more effectively damp the inter-area oscillations caused by increasing penetration of renewable resources and resulting uncertainty. Controls that use wide area signals, however, are not always reliable since communication systems are vulnerable to disruptions. As a result of which the power system reliability could also be vulnerable. To counteract communication failures, this paper presents an approach to build resiliency in the physical system by designing a robust control framework that incorporates a hierarchical set of control signals. This framework consists of multiple single-input-single- output (SISO) supplementary damping controllers (SDCs) associated with a static VAr compensator (SVC). When one signal in the hierarchy fails due to a communication failure, the control automatically utilizes another available signal through an alternative communication route to continue stabilizing the system. Simulations on the IEEE 50-generator system have demonstrated that the proposed control framework stabilizes the system and improves control resiliency in response to communication interruptions.