This dissertation embodies a comprehensive approach towards resilient monitoring of frid events using Structure Preserving Energy Functions (SPEFs) and introduces a novel control architecture in Multi Terminal Direct Current (MTDC) grids, for inter-area oscillation damping and achieving robustness to AC as well as DC side, post-contingency events in the modern power grid. This work is presented as a collection of several publications which investigate and address the proposed research topics. At first, SPEFs are derived for multi-machine IEEE benchmark models with the help of the Wide-Area Measurements (WAMs). A physics-based hybrid approach to develop one-to-one mapping between properties of energy function components with respect to the type of fault in the system is introduced. The proposed method is tested offline on a IEEE-39 bus, New England Test System (NETS), with particular interest in monitoring the most sensitive energy functions during relay misoperations. Such events can be precipitated by zone 3 trips in distance relays due to load encroachment during stressed conditions. These might include a genuine misoperation, a false trip due to cyber-attacks, or a load encroachment, all of which are undesirable under normal operating circumstances. An online monitoring scheme is introduced in an actual blackout simulation in the Western Electricity Coordinating Council (WECC) to examine what further indications these energy function components can provide, especially during a cascading sequence, and how they could supervise critical tripping decisions by distance relays. Next, a futuristic grid comprised of Voltage Source Converter (VSC) based AC-MTDC is considered due to its recent proliferation in integrating offshore wind farms to onshore grids, and additionally improving strength of weak AC grids. A robust control is designed using the converter station poles as actuators to provide damping support to the surrounding AC grid. Further, a design problem is envisioned and implemented that introduces disturbance rejection into control architecture by designing a novel explicitly modeled disturbance plant in the Linear Matrix Inequality (LMI) framework. Finally, a novel robust inter-area oscillation damping controller is designed that proves its effectiveness in inter-area mode settling times, and provides robustness to (n-1) contingencies in the AC as well as the DC side of the meshed AC-MTDC grid.