A 'practical' observer for nonlinear systems

In this paper, a 'practical' observer for nonlinear systems is given. Namely, it is shown that if the output and its time derivatives up to a sufficiently high finite order are bounded and the initial estimation error is sufficiently small, then the proposed observer is such that the estimation error can be made arbitrarily small for all sufficiently large times. Differently from other observers presented in the literature, the proposed observer does not require either global injectivity of the observability map or the knowledge of its local inverse.