Linearization by generalized input-output injection

The problem under interest is the linearization of nonlinear MIMO systems by generalized input-output injection in order to design observers with linear error dynamics. The method is based on the study of the structure of the input-output differential equations; thus, the problem is solved as a realization problem. In this note, one considers the linearization under two kinds of inout-output injection. In the first case, the transformation depends on the output and time derivatives of the input, whereas in the second case, derivatives of both the input and the output are considered. Necessary and sufficient conditions are obtained which generalize the ones on standard input-output injection linearization.