Luenberger observers for nonlinear controlled systems

We show how the (original) Luenberger methodology presented in [1] for autonomous linear systems can be used to design causal observers for controlled non linear systems. Their implementation relies on the resolution of a time-varying PDE, the solutions of which transform the dynamics into linear asymptotically stable ones. We prove the existence and injectivity (after a certain time) of such transformations, under a differential observability assumption. We also show on practical examples how this PDE can be solved and how the observability assumption can be checked.