An Immersion-Based Observer Design for Rank-Observable Nonlinear Systems

Dynamic extension without inversion for observers

“…It is used also, for instance in [6], [12], for uniformly observable systems when the order of differential observability is larger than the system state dimension to obtain an observer form to which the paradigm of high gain observers applies. In [5], Besançon and Ticlea take advantage of the degrees of freedom given by dynamic extension to obtain a form, called state affine up to triangular nonlinearity, to which Kalman-like observers can be applied. In [2], the authors show that, by going to dimension 2(n + 1) when the system state dimension is n, it is possible to obtain an observer with linear dynamic.…”

Nonlinear robust observer design using an invariant manifold approach

“…The approach presented in this paper requires the existence of a manifold that is invariant and attractive [32,33,34,35,36]. The manifold is made invariant by a nonlinear filter and attractive by proper selection of mapping functions.…”

Homogeneous approximations and local observer design

“…Conditions for the transformation of nonlinear systems into more general forms than exact linear systems have been explored. These classes of systems consists in systems which are made up of a particular linear part and a nonlinear part satisfying some Keywords and phrases: homogeneity, approximations, local observer conditions, and are characterized using algebro-geometric tools, see [3,5,10,21,24] for example. The common point in all these approaches is that the output function is always linearized, hence, this still restrict the class of systems considered while it allows to obtain global or semi-global convergence.…”