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We consider the tracking problem of unknown, robustly stabilizable, multi-input multi-output (MIMO), affine in the control, nonlinear systems with guaranteed prescribed performance. By prescribed performance we mean that the tracking error converges to a predefined arbitrarily small residual set, with convergence rate no less than a prespecified value, exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants. Utilizing an output error transformation, we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system, provided that initially the transformed system is well defined. Consequently, a switching robust control Lyapunov function (RCLF)-based adaptive, state feedback controller is designed, to solve the stated problem. The proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable. Simulations illustrate the approach.