Observers design for discrete-time Lipschitz nonlinear systems. State of the art and new results

This note addresses the problem of observers design for Lipschitz nonlinear systems in the discrete-time case. The main objective of this work is to clarify and correct some recent results in this field. After a state of the art, some analytical comparisons are provided. On the other hand, a new Linear Parameter Varying (LPV) technique is proposed to reduce the conservatism related to the classical observer design methods. A numerical example is given in order to show the performance of the proposed LPV method.