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Output Feedback Stabilization of Unstable Heat Equations with Time Delay in Boundary Observation

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  • Kun-Yi Yang
  • Lan Chen
  • Francisco Rossomando

Abstract

In this paper, an unstable heat equation where the observation signal suffers from a given time delay has been considered. In order to remove the unstable boundary condition, the original system has been converted into the stabilizing system by backstepping transformation under which the form of the stabilizing controller can be obtained. For the sake of overcoming instability produced by the time delay, firstly, we construct the Luenberger observer and design the predictor. Then, the estimated output feedback controllers have been obtained based on the observer and predictor systems. It is shown that the closed-loop system is stable exponentially. At last, numerical simulations have been given to illustrate the effectiveness of the stabilizing output feedback controllers.

Suggested Citation

  • Kun-Yi Yang & Lan Chen & Francisco Rossomando, 2022. "Output Feedback Stabilization of Unstable Heat Equations with Time Delay in Boundary Observation," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-11, March.
    • Handle: RePEc:hin:jnlmpe:6973646
    DOI: 10.1155/2022/6973646
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