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A real-time stabilizing control method for responding to N-K contingencies, with large K, is developed utilizing network and machine time-synchronized measurements. The controls follow an optimality principle in driving rotor-angles to an acceptable equilibrium point, at minimum cost, by predicting state response trajectory to a collection of stepped structural changes, from an admissible set, according to a defined model. A cost metric suitable for mitigating rotor-angle instability is developed. Non-idealities in modeling, measurement latency, control availability, and actuation success are investigated. It is shown how control over system structure in a feedback formulation increases the capability to handle higher order contingencies. As an experimental example, a set of simultaneous N-3 transient stability related contingencies are stabilized for the IEEE 39-bus system. Furthermore, the response after control actuation failure is investigated and it is shown that the system remains driven to a valid stable equilibrium point.