Magnon-based electronic devices can transmit information and energy via the transfer of spin angular momentum without relying on the movement of charge, thereby providing material and physical foundations for the research and development of low-power devices. This paper summarizes the research on magnon-magnon coupling effect, spin wave dispersion relation and the corresponding device applications in perpendicularly magnetized multilayer systems. First, a magnetization dynamics model is established based on the Landau-Lifshitz equation for coupled multilayer systems with perpendicular magnetic anisotropy. It is verified that symmetry breaking serves as the core mechanism of magnon-magnon coupling. Then, the magnon-magnon coupling effect and frequency gap under the T-type magnetic configuration are observed in two perpendicularly magnetized systems, and the nonreciprocity of spin waves is investigated. Finally, on the basis of theoretical and experimental research, device applications are further developed. By regulating the ON and OFF states of magnon-magnon coupling via magnetic field orientation, a switchable magnonic band-stop filter device is successfully fabricated, which demonstrates excellent operational repeatability and stable performance. This work summarizes the investigation path from physical mechanism, material system to device design, providing theoretical foundations and technical schemes for low-power magnon information processing and microwave functional devices.