Stabilization of diffusion equations under sampled-data spatially averaged measurements

Netzer Bar Am*, Emilia Fridman

*Corresponding author for this work

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

Abstract

We develop distributed sampled-data control for parabolic systems governed by 1-d semilinear diffusion-convection equations. We suggest a sampled-data controller design, where the sampling intervals in time and in space are bounded. The network of N stationary sensing devices provide spatially averaged state measurements over the sampling spatial intervals. Our sampled-data static output feedback enters the equation through N shape functions (which are localized in the space) multiplied by the corresponding state measurements. Sufficient conditions for the exponential stability of the closed-loop system are derived via direct Lyapunov-Krasovskii method in terms of Linear Matrix Inequalities (LMIs). By solving these LMIs, upper bounds on the sampling intervals that preserve the exponential stability can be found.

Original languageEnglish
Title of host publicationROCOND'12 - 7th IFAC Symposium on Robust Control Design
PublisherIFAC Secretariat
Pages307-312
Number of pages6
EditionPART 1
ISBN (Print)9783902823038
DOIs
StatePublished - 2012
Event7th IFAC Symposium on Robust Control Design, ROCOND'12 - Aalborg, Denmark
Duration: 20 Jun 201222 Jun 2012

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
Volume7
ISSN (Print)1474-6670

Conference

Conference7th IFAC Symposium on Robust Control Design, ROCOND'12
Country/TerritoryDenmark
CityAalborg
Period20/06/1222/06/12

Keywords

  • Distributed parameter systems
  • LMIs
  • Lyapunov method
  • Sampled-data control

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