Non-linear observer design by transformation into a generalized observer canonical form

An observer design method for a certain class of non-linear single output systems is introduced. The characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non-linear system is approximated by a linear one. The present paper deals with the derivation of a transformation of the considered non-linear system into a generalized observer canonical form (GOCF) which enables a systematic observer design similar to the linear one based on the well-known linear observer canonical form. To assign conditions for its existence, the transformation into the GOCF is carried out in two steps via a generalized observability canonical form (GOBCF). In contrast to previous forms used for linear systems, the two non-linear canonical forms presented here also depend on the time derivatives of the input variables. This means that the resulting observer has to be supplied, not only with the input and output variables of the given system, but also with derivatives of the input variables. However, a final example shows that it is possible to eliminate those derivatives in special cases.