Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs

Abstract : We solve in this article the problem of robust output feedback regulation for a system composed of two hyperbolic equations with collocated input and output in presence of a general class of disturbances and noise. Importantly, the robustness of the controller is considered with respect to delays in the actuation and in the measurements but also with respect to uncertainties on parameters, most importantly transport velocities. We show that it is necessary to consider these three types of uncertainty simultaneously as it is the only way to ensure the existence of non-zero robustness margins. The proposed control law introduces three degrees of freedom (by means of tuning parameters) on which we give general conditions to guarantee the existence of robustness margins. Provided that these conditions are satisfied, these tuning parameters enable a trade-off between performance and robustness, between disturbance rejection and sensitivity to noise. The existence of robustness margins and the Input To State Stability of the system are proved combining backstepping transformations (which are used to rewrite the considered system as a neutral system) and classical complex analysis techniques.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01997396
Contributeur : Jean Auriol <>
Soumis le : lundi 28 janvier 2019 - 23:57:04
Dernière modification le : jeudi 31 janvier 2019 - 01:32:04
Document(s) archivé(s) le : lundi 29 avril 2019 - 20:52:59

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  • HAL Id : hal-01997396, version 1

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Jean Auriol, Di Meglio. Robust output feedback stabilization for two heterodirectional linear coupled hyperbolic PDEs. 2019. ⟨hal-01997396⟩

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