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Control systems for safety-critical applications, including the ones relying on adaptive elements, have to be certified against strict performance and safety requirements. This study presents a practical approach for the design of a neuro-adaptive element with the specific purpose of safely recovering the performance of a reference model in presence of bounded uncertainties. The boundedness of the tracking error vector within an a-priori specified compact domain is enforced by applying robust invariant set analysis to the uncertain linear plant where the adaptive neural contribution is considered as an amplitude-bounded persistent disturbance. In this framework, tracking error requirements are specified via a set of LMI constraints and maximal allowed amplitudes for the adaptive control are computed using a numerical LMI solver. A specific neural network on-line learning and output confinement algorithm is also proposed to keep the adaptive control within selected amplitudes; as a result, the overall closed loop system has a guaranteed worst-case transient response. The proposed approach has been successfully applied to the design of a multi input multi output (MIMO) augmentation adaptive element that improves the performance of a pre-existing tracking controller for a research aircraft model.