Stabilization of ODE with hyperbolic equation actuator subject to boundary control matched disturbance

Hua Cheng Zhou, Bao Zhu Guo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation with external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the disturbance is estimated through a disturbance estimator with both time-varying high gain and constant high gain, and the disturbance is canceled online in the feedback loop. It is shown that the resulting closed-loop system with time-varying high gain is asymptotically stable and is practically stable with constant high gain. By SMC approach, the existence and uniqueness of the solution for the closed loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented. The resulting closed-loop system is shown to be exponentially stable. The numerical experiments are carried out to illustrate effectiveness of the proposed control law.

Original languageEnglish
Pages (from-to)12-26
Number of pages15
JournalInternational Journal of Control
Issue number1
StatePublished - 2 Jan 2019
Externally publishedYes


  • 35L02
  • 37L15
  • 93B51
  • 93B52
  • 93D15
  • Active disturbance rejection control
  • boundary feedback control
  • sliding mode control
  • stabilisation


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