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Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback

Christophe Zhang 1, 2
2 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that if the system is controllable in a periodic Sobolev space of order greater than 1, then the system can be stabilized exponentially in that space and, for any given decay rate, we give an explicit feedback law that achieves that decay rate.
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Submitted on : Friday, September 4, 2020 - 6:39:41 PM
Last modification on : Tuesday, September 28, 2021 - 5:16:36 PM

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  • HAL Id : hal-01905098, version 3
  • ARXIV : 1810.11214

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Christophe Zhang. Internal rapid stabilization of a 1-D linear transport equation with a scalar feedback. 2020. ⟨hal-01905098v3⟩

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