In this study, we aimed to develop a smart mattress for continuous health monitoring, utilizing the theory of inventive problem solving (TRIZ) to guide its innovative design. The system employs sensors to collect real-time heart rate and respiratory data, which are processed using finite impulse response filters and advanced signal processing techniques to accurately obtain heart rate and respiratory frequency. The physiological signals are transmitted to a cloud server, creating a comprehensive health management system that provides health monitoring, alert notifications, and management services through web platforms and mobile applications for both individuals and institutions, thereby enhancing the quality of health management. The smart mattress was validated through comparative analysis, demonstrating no significant differences in heart rate (p = 0.059) and respiratory rate (p = 0.170) measurements compared with medical-grade devices. In this research, we present an integrated hardware and software solution for smart devices and health management systems, applicable in various settings, including personal homes, healthcare institutions, and nursing facilities. The techniques and design principles employed in this study offer valuable insights and references for related research in health monitoring and management systems, with the potential for broader applications.