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This paper investigates the output feedback boundary control ofreaction-diffusion equations with either distributed or boundary measurement bymeans of a finite-dimensional observer. A constructive method dealing with thedesign of finite-dimensional observers for the feedback stabilization ofreaction-diffusion equations was reported in a recent paper in the case whereeither the control or the observation operator is bounded and also satisfiescertain regularity assumptions. In this paper, we go beyond by demonstratingthat a finite-dimensional state-feedback combined with a finite-dimensionalobserver can always be successfully designed in order to achieve the Dirichletboundary stabilization of reaction-diffusion PDEs with a either Dirichlet orNeumann boundary measurement.

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