Practical and Polytopic Observers for Nonlinear Uncertain Systems
Résumé
For a class of dynamical systems, with uncertain nonlinear terms considered as «unknown inputs», we give sufficient conditions for observability. We show also that there does not exist any exact observer independent of the unknown inputs. Under the additional assumption that the uncertainty is bounded, we build practical observers whose error converges exponentially towards an arbitrary small neighborhood of the origin. For the general case, when the system might be not observable with unknown inputs, we build polytopic observers providing time-varying bounds (depending on the uncertainty bounds) on the state variables. We illustrate these results on a biological model of a structured population.