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International audienceThis paper deals with the stability study of Partial Differential nonlinear Equation (PDE) of Saint-Venant. The proposed approach is based on the Multi-Models concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows to describe the dynamic of this nonlinear system in infinite dimension over a wide operating range. A stability analysis of the nonlinear PDE of Saint-Venant is proposed both by the use of Linear Matrix Inequality (LMI) and an Internal Model Boundary Control (IMBC) structures. The method is applied both in simulations and real experimentations through a micro channel, illustrating thus the theoretical results developed in the paper

A multi-model approach to Saint-Venant equations: A stability study by LMIs