A robust adaptive observer for nonlinear systems with unknown inputs and disturbances

We present a simple robust adaptive observer for systems with unknown inputs. The class of systems includes partially linear systems with differentiable non-linearities provided that the solutions are bounded (the bound is unknown). Parametric uncertainty and additive disturbances are considered where the parameters are piece-wise constant. It is also assumed that measurable outputs are corrupted by noise. We show under certain necessary and sufficient conditions convergence of the estimation errors.