Robustness of VS-MRAC with respect to unmodeled dynamics and external disturbances

A variable structure model reference adaptive controller (VS-MRAC) using only input and output measurements was previously proposed and was shown to be globally asymptotically stable with superior transient behavior and disturbance rejection properties. In the present work a singular perturbation approach is used to establish the robustness of the controller in the presence of unmodeled dynamics (parasitics) and disturbances. A novel Lyapunov-based technique is developed to analyze the overall system, and it is shown that, for sufficiently small parasitics, the system remains stable and the output error is small in some sense. It is shown that no explicit restriction appears in the derivative of the reference signal, as opposed to certain results found in the literature of adaptive control