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The proposed method trains a neural Koopman embedding, a deep neural network that approximates the state of the embedded bilinear system for nonlinear missile dynamics using trajectory data. This Koopman-embedded bilinear model enables the systematic design of a state-dependent Riccati equation-based controller with local stability guarantees. The proposed method facilitates a full-envelope missile control design without the intricate synthesis of multiple controllers required for gain scheduling. 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