ODE compensation for an unstable heat equation

In this paper, an ODE dynamic feedback control is designed to compensate an unstable heat equation. Using Nyquist criterion for DPS, the relationship between the number of unstable poles and that of turns around the point (−1,0) clockwise determines the effect of dynamic compensator clearly. Next, the well-posedness of the closed-loop system is verified by semigroup theory and Riesz basis method. At the same time, the system is proved to be exponentially stable. Finally, some numerical simulations are presented to demonstrate that the closed-loop system is stable and our proposed dynamic controller is an efficient tool to stabilize unstable heat equations.