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

Valérie Dos Santos Martins; Mickael Rodrigues; Mamadou Diagne

International Journal of Applied Mathematics and Computer Science (2012)

- Volume: 22, Issue: 3, page 539-550
- ISSN: 1641-876X

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topValérie Dos Santos Martins, Mickael Rodrigues, and Mamadou Diagne. "A multi-model approach to Saint-Venant equations: A stability study by LMIs." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 539-550. <http://eudml.org/doc/244061>.

@article{ValérieDosSantosMartins2012,

abstract = {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.},

author = {Valérie Dos Santos Martins, Mickael Rodrigues, Mamadou Diagne},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Saint-Venant equation; multi-model; LMIs; infinite dimensional system; exponential stability; strongly continuous semigroup; internal model boundary control},

language = {eng},

number = {3},

pages = {539-550},

title = {A multi-model approach to Saint-Venant equations: A stability study by LMIs},

url = {http://eudml.org/doc/244061},

volume = {22},

year = {2012},

}

TY - JOUR

AU - Valérie Dos Santos Martins

AU - Mickael Rodrigues

AU - Mamadou Diagne

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2012

VL - 22

IS - 3

SP - 539

EP - 550

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/244061

ER -

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