ON FEEDBACK EQUIVALENCE OF A PARAMETERIZED FAMILY OF NONLINEAR-SYSTEMS

The following question is considered for a smoothly parameterized fami ly of control systems: Does there exist a smooth family of transformat ions (feedback only, feedback plus diffeomorphism, or feedback plus di ffeomorphism with some restrictions on the parameter dependence of the diffeomorphism, called ''matching conditions'') changing the systems of the family into a single one? Some abstract necessary and sufficien t conditions are given, under which an explicit construction of the tr ansformation is proposed. Both local and global results are obtained. No constant rank assumption is needed for the general conditions, but they can be translated more explicitly under such assumptions.