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Two asymptotic tracking controllers are designed in this paper, which combine model reference adaptive control and dynamic inversion methodologies in conjunction with the robust integral of the signum of the error (RISE) technique for output tracking of an aircraft system in the presence of parametric uncertainty and unknown, nonlinear disturbances, which are not linearly parameterizable (non-LP). The control designs are complicated by the fact that the control input is multiplied by an uncertain, non-square matrix. A robust control design is presented first, in which partial knowledge of the aircraft model along with constant feedforward estimates of the unknown input parameters are used with a robust control term to stabilize the system. Motivated by the desire to reduce the need for high-gain feedback, an adaptive extension is then presented, in which feedforward adaptive estimates of the input uncertainty are used. These results show how asymptotic tracking control can be achieved for a nonlinear system in the presence of a non-square input matrix containing parametric uncertainty and nonlinear, non-LP disturbances. Asymptotic output tracking is proven via Lyapunov stability analysis, and high-fidelity simulation results are provided to verify the efficacy of the proposed controllers.