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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 and to propose a new design methodology. This is based on the reformulation of the Lipschitz property using some mathematical tools. This reformulation is a relevant and useful Lipschitz condition, which leads to less restrictive LMI conditions. To show the superiority of this latter, two numerical examples are presented.
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