Removing input derivatives in generalized state-space systems: a linear algebraic approach

The problem of lowering the orders of input derivatives in generalized state space systems by generalized state transformations is studied through the language of differential forms. Necessary and sufficient conditions are given for the local existence of such transformation. The sufficiency part of the proof gives a constructive procedure (up to the integration of one-forms) for finding these generalized state transformations. In particular case, these conditions show when it is possible to transform a generalized state space representation into the classical state equations