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Motivated by recent advance in designing robust adaptive controllers and in dealing with uncertain dynamical systems, a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented. The implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking. It is shown that global stability of the overall system is achieved under no assumption of persistency of excitation, and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly. In the ideal case, the residual set degenerates to a single null point and the convergence can be achieved in finite time without any requirement of persistency of excitation.