Transformation Into Triangular Forms
This chapter raises the question of transforming a nonlinear system into a triangular form. It is recalled that a differential observability condition enables to transform a system into a phase-variable form (with a nonlinearity on the last line only) but via a map that depends on the derivatives of the input, which may not be desirable. To suppress this dependence, the famous uniform observability (“observability for any input”) is necessary to ensure the triangularity of the target form. However, it is not sufficient to obtain a Lipschitz triangular form, and it may only give a continuous triangular form. The link between this Lipschitzness and the order of differential observability of the drift system is investigated.