Boundary feedback stabilization and Riesz basis property of a 1-d first order hyperbolic linear system with L∞-coefficients

Boumediène Chentouf, Jun Min Wang

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

This paper deals with the boundary feedback stabilization problem of a wide class of linear first order hyperbolic systems with non-smooth coefficients. We propose static boundary inputs (actuators) which lead us to a closed loop system with non-smooth coefficients and non-homogeneous boundary conditions. Then, we prove the exponential stability of the closed loop system under suitable conditions on the coefficients and the feedback gains. The key idea of the proof is to combine the regularization techniques with the characteristics method. Furthermore, by the spectral analysis method, it is also shown that the closed loop system has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition is deduced.

Original languageEnglish
Pages (from-to)1119-1138
Number of pages20
JournalJournal of Differential Equations
Volume246
Issue number3
DOIs
Publication statusPublished - Feb 1 2009

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Keywords

  • C-semigroup
  • First order hyperbolic linear system
  • L-coefficients
  • Regularization method
  • Riesz basis
  • Stability

ASJC Scopus subject areas

  • Analysis

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