LPV approach to continuous and discrete nonlinear observer design

In this paper we propose a new systematic design of nonlinear observers for Lipschitz nonlinear systems subject to nonlinear outputs. The new design method is dedicated to both continuous-time and discrete-time nonlinear systems having Lipschitz nonlinear outputs. By the use of the global Lipschitz property, the nonlinear system is rewritten as a linear parameter varying system subject to a linear parameter varying output. Based upon this new representation a Luenberger-like observer is designed without any linearization of the dynamics of the system or the observer. Robustness with respect to noisy measurements is also considered in a LMI setting. The present contribution is an extension of the results given in a previous work of the author. We show that the existence of the observer gain is related to the solvability of a Linear Parameter Varying optimization problem and therefore, the requirement of linearization of the observation error is not needed even if the measured output is not linear. The novelty and the efficacy of the proposed design is approved by illustrative case studies.