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The paper deals with output feedback stabilization of exponentially stablesystems by an integral controller. We propose appropriate Lyapunov functionalsto prove exponential stability of the closed-loop system. An example ofparabolic PDE (partial differential equation) systems and an example ofhyperbolic systems are worked out to show how exponentially stabilizingintegral controllers are designed. The proof is based on a novel Lyapunovfunctional construction which employs the forwarding techniques.

Adding integral action for open-loop exponentially stable semigroups and application to boundary control of PDE systems