Feedback equivalence for a class of nonlinear singularly perturbed systems

The feedback equivalence for a class of nonlinear singularly perturbed systems is studied. This is accomplished by reducing the full-order problem into a lower order exact problem using the slow manifold theory. This facilitates development of an approximate and simpler linearizing control strategy achievable to an arbitrary degree of accuracy. It is shown that, in contradistinction to systems with unobservable parasitics where a state-dependent transformation and a static feedback controller are required, for systems with observable parasitics a state- and control-dependent transformation and a dynamic feedback controller should be used to transform the exact system into a linear system in controller and observer form