Observer Synthesis for Uncertain Nonlinear Systems. Application to Waste-Water Treatment Plants

The paper proposes an observer synthesis for uncertain nonlinear systems, described by multimodels with unmeasurable premise variables, affected by unknown inputs. A proportional multi-integral observer is considered in order to estimate the system states and the unknown inputs and minimize the influence of the model uncertainties. The stability analysis and the observer synthesis are expressed through linear matrix inequalities based on the Lyapunov method. The performances of the proposed observer synthesis method are highlighted through the application to a waste-water treatment plant model, which is an uncertain nonlinear system affected by unknown inputs.