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The AC frequency in electrical power systems is conventionally regulated by synchronous machines. The gradual replacement of these machines by asynchronous renewable-based generation, which provides] little or no frequency control, increases system uncertainty and risk of instability. This poses hard limits on the proportion of renewables that can be integrated into the system. To address this issue, in this paper, we develop a framework for performing frequency control in power systems with arbitrary mixes of conventional and renewable generation. Our approach is based on a robust stability criterion that can be used to guarantee the stability of a full power system model based on a set of decentralised tests, one for each component in the system. It can be applied even when using detailed heterogeneous component models and can be verified using several standard frequency response, state-space, and circuit theoretic analysis tools. By designing decentralised controllers for individual components to meet these decentralised tests, strong apriori robust stability guarantees, that hold independently of the operating point and remain valid even as components are added to and removed from the grid, can be given. This allows every component to contribute to the regulation of system frequency in a simple and provable manner. Notably, our framework certifies the stability of several existing (non-passive) power system control schemes and models, and allows for the study of robustness with respect to delays.