Observers for continuous-time Lipschitz nonlinear systems. Analysis and comparisons

This paper addresses the problem of observer design for Lipschitz nonlinear systems via LMI. The goal of this note is to clarify some recent results in this field. Some comparisons are provided and new design methodology is proposed. This new design is based on the reformulation of the Lipschitz property using some mathematical tools. This reformulation leads to less restrictive LMI conditions. To show the superiority of this latter, two numerical examples are presented.