<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Automatic and Process Control Laboratory (LAGEP) University of Lyon 1, CNRS, UMR 5007, Villeurbanne F-69622, France

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"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...

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

Published Online: Sep 28, 2012

Page range: 539 - 550

DOI: https://doi.org/10.2478/v10006-012-0041-6

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

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Sep 28, 2012

Page range: 539 - 550

DOI: https://doi.org/10.2478/v10006-012-0041-6

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

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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