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Finite-time stabilization of 2*2 hyperbolic systems on tree-shaped networks

Abstract : We investigate the finite-time boundary stabilization of a 1-D first order quasilinear hyperbolic system of diagonal form on [0,1]. The dynamics of both boundary controls are governed by a finite-time stable ODE. The solutions of the closed-loop system issuing from small initial data in Lip([0,1]) are shown to exist for all times and to reach the null equilibrium state in finite time. When only one boundary feedback law is available, a finite-time stabilization is shown to occur roughly in a twice longer time. The above feedback strategy is then applied to the Saint-Venant system for the regulation of water flows in a network of canals.
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https://hal.archives-ouvertes.fr/hal-00793728
Contributor : Lionel Rosier <>
Submitted on : Friday, February 22, 2013 - 7:22:32 PM
Last modification on : Thursday, April 9, 2020 - 5:08:12 PM
Document(s) archivé(s) le : Sunday, April 2, 2017 - 4:37:04 AM

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  • HAL Id : hal-00793728, version 1
  • ARXIV : 1302.5812

Citation

Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of 2*2 hyperbolic systems on tree-shaped networks. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2014, 52 (1), pp.143-163. ⟨hal-00793728⟩

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