FEEDBACK EQUIVALENCE FOR A CLASS OF NONLINEAR SINGULARLY PERTURBED SYSTEMS

One of the greatest obstacles and limitations in application of the current nonlinear control theory is its strong dependency on accurate models. Generally, more accurate representation of dynamic systems could create difficulties for satisfying the necessary and sufficient conditions in most of the present methodologies concerned with feedback equivalence and external linearization of nonlinear systems (e.g., flexible joint manipulators are not feedback linearizable by static feedback control, whereas the rigid manipulator models are indeed feedback linearizable). This calls for the development of more practical techniques. We believe that this note is a step towards this direction. In this note, 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 are obtained. © 1990 IEEE