AN INTRINSIC PROPERTY OF RELATIVE ORDER AND ITS APPLICATION

Although the very important concept of relative order is defined in di fferential geometric control with respect to an affine input-state-out put (I-S-O) system, it is rather the difference between the highest or ders of the derivative of output and that of input in the correspondin g input-output (I-O) systems. This is a direct generalization of the r esult in the case of the transfer function in linear control theory. T he relative order is proved to be an invariant of realization, and app lications in realization and minimal equivalence are discussed.