Pfaffian basis for affine nonlinear systems

Under a certain assumption on the controllability the concept of Pfaffian basis for affine nonlinear control systems is introduced. We show that this concept is relevant to the problem of total linearization, i.e., linearizing state and output equations simultaneously, and to the problem of input-output decomposed total linearization. In particular, we give necessary and sufficient conditions for both the total linearizability and the input-output decomposed total linearizability of affine nonlinear systems.