Controller design for chain-type wave network models with boundary delays

In this paper, we consider the design method of full-state integral feedback controllers, selecting appropriate target systems, establishing equivalent transformations, and completing the stability analysis of the original system while avoiding a large amount of complex calculations and proofs. This research attempts to establish a universally applicable controller design strategy that can not only eliminate the negative effects of system delays, but also ensure the closed-loop stability. Therefore, this paper further explores the applicability of this controller design strategy in complex PDE-coupled systems, seeks general patterns, and has further theoretical and practical value for the stability study of infinite-dimensional time-delay systems.