Local Input-to-State Stabilization of 1-D Linear Reaction-Diffusion Equation with Bounded Feedback

Aneel Tanwani 1 Swann Marx 2 Christophe Prieur 2
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : The problem of robust stabilization with bounded feedback control is considered for a scalar reaction-diffusion system with uncertainties in the dynamics. The maximum value of the control input acting on one of the boundary points has to respect a given bound at each time instant. It is shown that, if the initial condition and the disturbance satisfy the certain bounds (computed as a function of the bound imposed on the control input), then the proposed control respects the desired saturation level and renders the closed-loop system locally input-to-state stable, that is, the trajectories with certain bound on the initial condition converge to a ball parameterized by certain norm of the disturbance.
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Aneel Tanwani, Swann Marx, Christophe Prieur. Local Input-to-State Stabilization of 1-D Linear Reaction-Diffusion Equation with Bounded Feedback. 23rd International Symposium on Mathematical Theory of Networks and Systems (MTNS2018) , Jul 2018, Hong Kong, China. 6p. ⟨hal-01785104⟩

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