Boundary Observers for a Reaction-Diffusion System Under Time-Delayed and Sampled-Data Measurements

Anton Selivanov, Emilia Fridman

Research output: Contribution to journalArticlepeer-review

Abstract

We construct finite-dimensional observers for a one-dimensional reaction-diffusion system with boundary measurements subject to time-delays and data sampling. The system has a finite number of unstable modes approximated by a Luenberger-type observer. The remaining modes vanish exponentially. For a given reaction coefficient, we show how many modes one should use to achieve a desired rate of convergence. The finite-dimensional part is analyzed using appropriate Lyapunov-Krasovskii functionals that lead to linear matrix inequalitie (LMI)-based convergence conditions feasible for small enough time-delay and sampling period. The LMIs can be used to find appropriate injection gains.

Original languageEnglish
Article number8502078
Pages (from-to)3385-3390
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume64
Issue number8
DOIs
StatePublished - Aug 2019

Keywords

  • Boundary measurements
  • data sampling
  • observers
  • partial differential equations
  • time-delays

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