Geodesic
Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems
Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 5, pp. 1235-1260

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Hyperbolic systems in one-dimensional space are frequently used in the modeling of many physical systems. In our recent works we introduced time-independent feedbacks leading to finite stabilization in optimal time of homogeneous linear and quasilinear hyperbolic systems. In this work we present Lyapunov’s functions for these feedbacks and use estimates for Lyapunov’s functions to rediscover the finite stabilization results.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/30
Classification : 35F05, 35F15, 93C20, 93D05, 93D15, 93D23
Keywords: Hyperbolic systems, boundary controls, Lyapunov functions, backstepping, finite-time stabilization, optimal time 
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     author = {Coron, Jean-Michel and Nguyen, Hoai-Minh},
     title = {Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1235--1260},
     volume = {39},
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     year = {2022},
     doi = {10.4171/aihpc/30},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/30/}
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Coron, Jean-Michel; Nguyen, Hoai-Minh. Lyapunov functions and finite-time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 5, pp. 1235-1260. doi: 10.4171/aihpc/30

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