PDE-based observation and predictor-based control for linear systems with distributed infinite input and output delays

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This paper considers output feedback stabilization of linear systems with both distributed infinite input and output delays. We first propose a PDE-based observer to deal with distributed infinite output delays. The main idea is to transform infinite-delayed output into a transport PDE with a semi-infinite domain. It is proved that the resulted error systems are exponentially stable and thus the observer is effective. Furthermore, relying on the PDE-based observer, a predictor-based output feedback stabilization controller is provided. This work removes a restrictive condition on eigenvalues of open-loop system in the previous work, which is a distinctive advantage of this work. A simulation example is given to illustrate the effectiveness of our proposed observer and controller.