Immersion-based observer design for nonlinear systems

In this paper, it is shown how immersion can yield an appropriate structure for observer design for a large class of nonlinear systems. The appropriate structure is that of state affine system, up to triangular nonlinearity, which is shown to allow sonic exponential observer design under appropriate excitation on the one hand. On the other hand the observability rank condition is shown to be a sufficient condition for possible immersion into such a form, and a constructive procedure is provided. The whole methodology is illustrated by a couple of examples