With the model-based approaches gaining popularity in the development of complex systems, formal approaches for functional modeling have attracted a lot of attention. However, existing approaches for functional modeling do not involve structural states of a system, which often makes the functional models of such systems ambiguous and incomplete. To address this issue, research on a state-integrated approach for generalized functional modeling has been conducted. First, the State-Bahvior-Function model for components is proposed, which can represent the structural states, behaviors, and functions of a component. Thereafter, an approach for generalized functional modeling of systems is proposed, which can represent different structural states of a system, as well as the functions corresponding to the states of the system. Finally, the functional modeling process of a peeler centrifuge is provided as an example, which demonstrates that the state-integrated approach for generalized functional modeling can enable engineers to establish explicit and complete functional models of systems.