Boundary control of hyperbolic conservations laws using a frequency domain approach | Contrôle frontière de lois de conservations hyperbolique par une approche fréquentielle
2009
Litrico, X. | Fromion, Vincent | Gestion de l'Eau, Acteurs, Usages (UMR G-EAU) ; Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Centre international d'études supérieures en sciences agronomiques (Montpellier SupAgro)-AgroParisTech-Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF)-Institut de Recherche pour le Développement (IRD [France-Sud])-Centre International de Hautes Etudes Agronomiques Méditerranéennes - Institut Agronomique Méditerranéen de Montpellier (CIHEAM-IAMM) ; Centre International de Hautes Études Agronomiques Méditerranéennes (CIHEAM)-Centre International de Hautes Études Agronomiques Méditerranéennes (CIHEAM) | Institut National de la Recherche Agronomique (INRA)
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Show more [+] Less [-]English. The paper uses a frequency domain method for the boundary control of hyperbolic conservation laws. We show that the transfer function of the hyperbolic system belongs to the CallierDesoer algebra, which opens the way of sound results, and in particular to the existence of a necessary and sufficient condition for the closed loop stability and the use of Nyquist type test. We examine the link between inputoutput stability and exponential stability of the state. Specific results are then derived for the case of proportional diagonal boundary controllers. The results are illustrated in the case of diagonal boundary control of open channel flow.
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