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The paper presents the role of self-stabilization analysis in the design, verification and validation of the dynamics of an Adaptive Flight Control System (AFCS). Since the traditional self-stabilization approaches lack the flexibility to deal with the continuous adaptation of the neural network within the AFCS, the paper emphasizes an alternate self-stability analysis approach, namely Lyapunov's Second Method. A Lyapunov function for the neural network is constructed and used in presenting a formal mathematical proof that verifies the following claim: While learning from a fixed input manifold, the neural network is self-stabilizing in a Globally Asymptotically Stable manner. When dealing with variable data manifolds, we propose the need for a real-time stability monitor that can detect unstable state deviations. The test results based on the data collected from an F-15 flight simulator provide substantial heuristic evidence to support the idea of using a Lyapunov function to prove the self-stabilization properties of the neural network adaptation.