A singularly perturbed nonlinear system with a control input and a measured output is considered, under the supposition that a static nonlinear output feedback law is designed. It is shown that the operations 'compute the reduced-order system' (i.e., let the singular perturbation parameter μ = 0) and 'close the feedback loop' commute, i.e., the closed-loop reduced-order system is unambiguously determined. It is then shown that, if the reduced-order system associated with the original system has uncertainties matched with the input, a condition frequently used in the design of robust control systems, then the closed-loop reduced-order system enjoys the same property.
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