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

Authors: V. Perrollaz and L. Rosier, SIAM Journal on Control and Optimization, Vol 51 no 1, pp. 143--163, 21 January 2014 DOI: 10.1137/130910762
We investigate the finite-time boundary stabilization of a one-dimensional 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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author = {V. Perrollaz and L. Rosier},
title = {Finite-time stabilization of 2 x 2 hyperbolic systems on tree-shaped networks},
journal = {SIAM Journal on Control and Optimization},
volume = {52},
number = {1},
pages = {143-143},
year = {2014},