Observers design for uncertain Takagi–Sugeno systems with unmeasurable premise variables and unknown inputs. Application to a wastewater treatment plant

This article aims the observer synthesis for uncertain nonlinear systems and affected by unknown inputs, represented under the multiple model (MM) formulation with unmeasurable premise variables. A proportional integral observer (PIO) is considered. In order to design such an observer, the nonlinear system is transformed into an equivalent MM form. The Lyapunov method, expressed through linear matrix inequality (LMI) formulation, is used to describe the stability analysis and for the observer synthesis. An application to a model of wastewater treatment plant (WWTP) is considered and the performances of the proposed approach are illustrated through numerical results.

► Here, a proportional integral observer is designed for uncertain nonlinear systems with unknown inputs.
► The nonlinear system is equivalently written as a multiple model with unmeasurable premise variables.
► The state and unknown input estimation are simultaneously obtained.
► The influence of the model uncertainties is minimized with the L2 approach.
► The chosen application is a wastewater treatment plant.