Boundary Delayed Observer-Controller Design for Reaction-Diffusion Systems

Rami Katz, Emilia Fridman*, Anton Selivanov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider delayed boundary stabilization of a one-dimensional reaction-diffusion equation under boundary delayed measurements. We design an observer-based control law via the modal decomposition approach. The observer is governed by a partial differential equation, which leads to separation of the observer and the controller design. We suggest a network-based implementation of the controller in the presence of two networks: from sensor to controller, and from the controller to actuator. To reduce the workload of the second network, we suggest a novel switching-based dynamic event-triggering mechanism. We extend the results to the vector case and illustrate their efficiency by anumerical example.

Original languageEnglish
Article number8998162
Pages (from-to)275-282
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number1
StatePublished - Jan 2021


  • Parabolic PDEs
  • delay
  • event-triggered control
  • modal decomposition
  • observer-based control


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