Regional Stabilization of the 1-D Kuramoto-Sivashinsky Equation via Modal Decomposition

Rami Katz, Emilia Fridman

Research output: Contribution to journalArticlepeer-review

Abstract

In this letter, we suggest regional stabilization of the semilinear 1D KSE under nonlocal or boundary actuation. We employ modal decomposition and derive regional H^{1} stability conditions for the closed-loop system. Given a decay rate that defines the number of state modes in the controller, we provide LMIs for finding the the controller gain as well as a bound on the domain of attraction. In the case of boundary control, we suggest a dynamic extension with a novel internally stable dynamics. The latter allows to enlarge a bound on the domain of attraction. Numerical examples illustrate the efficiency of the method.

Original languageEnglish
Pages (from-to)1814-1819
Number of pages6
JournalIEEE Control Systems Letters
Volume6
DOIs
StatePublished - 2022

Keywords

  • Distributed parameter systems
  • boundary control
  • nonlinear parabolic PDEs

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