  The design of a nonlinear Luenberger observer for a parametrized linear SISO
(single-input single-output) system is studied. From an observability
assumption of the system, the existence of such an observer is concluded. In a
second step, a novel algorithm for the identification of such systems is
suggested and is implemented on a third order system. Compared to the adaptive
observer available in the litterature, it has the advantage to be of low
dimension and to admit a strict Lyapunov function. This is a long version of a
paper which is published in IEEE TAC 2017.
