On the relation between approaches for boundary feedback control of hyperbolic systems

Stabilization of partial differential equations is a topic of utmost importance in mathematics as well as in engineering sciences. Concerning one dimensional problems there exists a well developed theory. Due to numerous important applications the interest in boundary feedback control of multi-dimensional hyperbolic systems is increasing. In the present work we want to discuss the relation between some of the most recent results available in the literature. The key result of the present work is to show that the type of system discussed in Yang and Yong (2024) identifies a particular class which falls into the framework presented in Herty and Thein (2024).