Stabilization of linearized Korteweg-de Vries systems with anti-diffusion

Shuxia Tang, Miroslav Krstic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Scopus citations

Abstract

In this paper, backstepping boundary controllers are designed for a class of linearized Korteweg-de Vries systems with possible anti-diffusion, and the resulting closed-loop systems can achieve arbitrary exponential decay rate. Semigroup of linear operators is constructed in analyzing well-posedness and stability of the target systems, and mathematical induction is used in proving existence of kernel functions. An example is also presented, which illustrates performance of the controller. The decay rate estimate derived in this paper is not necessarily equal to decay rate, which can be seen from the appendix.

Original languageEnglish
Title of host publication2013 American Control Conference, ACC 2013
Pages3302-3307
Number of pages6
StatePublished - Sep 11 2013
Event2013 1st American Control Conference, ACC 2013 - Washington, DC, United States
Duration: Jun 17 2013Jun 19 2013

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Conference

Conference2013 1st American Control Conference, ACC 2013
CountryUnited States
CityWashington, DC
Period06/17/1306/19/13

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Keywords

  • Antidiffusion
  • Arbitrary exponential decay rate
  • Backstepping
  • Linearized Korteweg-de Vries systems
  • Semigroup of linear operators

Cite this

Tang, S., & Krstic, M. (2013). Stabilization of linearized Korteweg-de Vries systems with anti-diffusion. In 2013 American Control Conference, ACC 2013 (pp. 3302-3307). [6580341] (Proceedings of the American Control Conference).