Observer design for linear processes model with implicit nonlinear output map

Linear dynamical models with nonlinear output maps can represent a wide range of industrial processes. In particular, in many applications the output maps are defined in terms of an implicit function. In this context, it is necessary to design an observer which does not require to invert explicitly the output map in order to obtain the estimated output. The proposed approach considers this particular requirement, a nonlinear perturbation term associated to the dynamic part, characterized in terms of a Lipschitz constant, and a continuous differentiable output map. The stability of the non-linear error dynamic is analysed by transforming the error dynamic into a Linear Parameter Varying (LPV) system. Two representative examples, i.e. neutralization process and conductivity estimation, illustrate the main features of the design process and the performance obtained with the proposed observer.