Global complete observability and output-to-state stability imply the existence of a globally convergent observer

In this paper we consider systems which are globally completely observable and output-to-state stable. The former property guarantees the existence of coordinates such that the dynamics can be expressed in observability form. The latter property guarantees the existence of a state norm observer and therefore nonlinearities bounding function and local Lipschitz bound. Both allow us to build an observer from an approximation of an exponentially attractive invariant manifold in the space of the system state and an output driven dynamic extension. The state of this observer has the same dimension as the state to be observed. Its main interest is to provide convergence to zero of the estimation error within the domain of definition of the solutions.