Static Output Feedback Control of Heat Equations With Small Reaction Terms

This letter studies the static output feedback stabilization of constant coefficients heat equations by means of a proportional controller. We consider the case of a Dirichlet boundary control and Dirichlet boundary measurement. In this setting, we show that a simple proportional static output feedback control strategy can be successfully implemented for sufficiently small reaction terms. By duality, the same result applies to the case of a Neumann boundary control and Neumann boundary measurement.