Sampled-data control of semilinear 1-d heat equations ?

Emilia Fridman*, Anatoly Blighovsky

*Corresponding author for this work

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


A semilinear one-dimensional convection-diffusion equation with distributed control, coupled to the Dirichlet or to the mixed boundary conditions, is considered. A sampled-data controller design is developed, where the sampled-data (in time) measurements of the state are taken in a finite number of fixed sampling points in the spatial domain. Sufficient conditions for the exponential convergence of the state dynamics are derived in terms of Linear Matrix Inequalities (LMIs) depending on the bounds of the sampling intervals. The new method is based on the direct Lyapunov approach via Wirtinger's and Halanay's inequalities.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
StatePublished - 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670


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


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