Finite-dimensional observer-based boundary stabilization of reaction-diffusion equations with a either Dirichlet or Neumann boundary measurement

Abstract

This paper investigates the output feedback boundary control of reaction-diffusion equations with either distributed or boundary measurement by means of a finite-dimensional observer. A constructive method dealing with the design of finite-dimensional observers for the feedback stabilization of reaction-diffusion equations was reported in a recent paper in the case where either the control or the observation operator is bounded and also satisfies certain regularity assumptions. In this paper, we go beyond by demonstrating that a finite-dimensional state-feedback combined with a finite-dimensional observer can always be successfully designed in order to achieve the Dirichlet boundary stabilization of reaction-diffusion PDEs with a either Dirichlet or Neumann boundary measurement.

arXiv commentAccepted for publication in Automatica

References in corpus (3)

• Feedback stabilization of a 1D linear reaction-diffusion equation with delay boundary control
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Cited by in corpus (5)

• Predictor-Based Output Feedback Stabilization of an Input Delayed Parabolic PDE with Boundary Measurement
• Local output feedback stabilization of a Reaction-Diffusion equation with saturated actuation
• Backstepping for Partial Differential Equations:A Survey
• Finite-dimensional observer-based PI regulation control of a reaction-diffusion equation
• Nonlinear Boundary Output Feedback Stabilization of Reaction-Diffusion Equations