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

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 describ...

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Bibliographic Details
Published in:International journal of applied mathematics and computer science 2012-09, Vol.22 (3), p.539-550
Main Authors: Dos Santos Martins, Valérie, Rodrigues, Mickael, Diagne, Mamadou
Format: Article
Language:English
Subjects:
exponential stability
infinite dimensional system
internal model boundary control
LMIs
multi-model
Saint-Venant equation
strongly continuous semigroup
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Summary: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.
ISSN:2083-8492
1641-876X
2083-8492
DOI:10.2478/v10006-012-0041-6