International Journal of applied mathematics and computer science

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Paper details

Number 3 - September 2012
Volume 22 - 2012

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

Valérie Dos Santos Martins, Mickael Rodrigues, Mamadou Diagne

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

Saint-Venant equation, multi-model, LMIs, infinite dimensional system, exponential stability, strongly continuous semigroup, internal model boundary control