Stabilization of coupled Schrödinger and heat equations with boundary coupling

Jun Min Wang, Beibei Ren, Miroslav Krstic

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study stability of a Schrödinger equation with a collocated boundary feedback compensator in the form of a heat equation with a collocated input/output pair. We show that the spectrum of the closed-loop system consists only of two branches along two parabolas which are asymptotically symmetric relative to the line Reλ = Imλ (the 135° line in the second quadrant). The asymptotic expressions of both eigenvalues and eigenfunctions are obtained. The Riesz basis property and exponential stability of the system are then proved. Finally we show that the semigroup, generated by the system operator, is of Gevrey class δ ≥ 2. A numerical computation is presented for the distributions of the spectrum of the closed-loop system.

Original languageEnglish
Title of host publicationProceedings of the 30th Chinese Control Conference, CCC 2011
Pages986-991
Number of pages6
StatePublished - 2011
Event30th Chinese Control Conference, CCC 2011 - Yantai, China
Duration: Jul 22 2011Jul 24 2011

Publication series

NameProceedings of the 30th Chinese Control Conference, CCC 2011

Conference

Conference30th Chinese Control Conference, CCC 2011
CountryChina
CityYantai
Period07/22/1107/24/11

Keywords

  • Boundary control
  • Gevrey regularity
  • Heat equation
  • Schrödinger equation
  • Spectrum
  • Stability

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