Multivalued finite-time observers for a class of nonlinear systems

We consider a class of nonlinear systems which are not observable, and can have a finite number of indistinguishable trajectories. In general, this implies that a single-valued observer does not exist. In this paper we propose the construction of a multivalued observer, which is able to estimate the full set of indistinguishable trajectories. Moreover, it is also able to estimate all possible unknown inputs acting on the system. An application to a Magnetic levitation system is proposed as an illustrative example.