Robust Stabilization of Singularly Perturbed Nonlinear Systems

Consider a singularly perturbed nonlinear system endowed with a control input and suppose a static nonlinear feedback law is designed. We show that the operations 'compute the reduced order system' (i.e., let the singular perturbation parameter mu=0) and 'close the feedback loop' commute, i.e. the closed loop reduced-order system is unambiguously determined. We then show that, if the reduced order system associated with the original system is stabilizable or has uncertainties matched with the input (a condition frequently used in the design of robust controllers), then the closed loop reduced-order system enjoys the same property. As shown by an example, this result can be used to simplify the structure of a composite controller.