Input-to-state stabilization of coupled parabolic PDEs subject to external disturbances

Jun Min Wang, Han Wen Zhang*, Xiu Fang Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we are concerned with the input-to-state stabilization of coupled parabolic partial differential equations, which is suffering the disturbances in all channels. By using the sliding mode control integrated with the backstepping approach, we design two boundary feedback controllers to reject the matched boundary disturbances, stabilize the whole coupled system in the absence of unmatched disturbances and achieve the input-to-state stability property of the closed-loop system with respect to the unmatched disturbances. We show the existence of the generalized solutions of the closed-loop system in the Hilbert energy space. Some numerical simulations are presented to illustrate the effectiveness of the proposed controllers.

Original languageEnglish
Pages (from-to)185-218
Number of pages34
JournalIMA Journal of Mathematical Control and Information
Volume39
Issue number1
DOIs
Publication statusPublished - 1 Mar 2022

Keywords

  • ISS property
  • backstepping
  • coupled parabolic PDEs
  • disturbance rejection
  • generalized solutions

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