  Deploying safety-critical controllers in practice necessitates the ability to
modulate uncertainties in control systems. In this context, robust control
barrier functions -- in a variety of forms -- have been used to obtain safety
guarantees for uncertain systems. Yet the differing types of uncertainty
experienced in practice have resulted in a fractured landscape of
robustification -- with a variety of instantiations depending on the structure
of the uncertainty. This paper proposes a framework for generalizing these
variations into a single form: parameterized barrier functions (PBFs), which
yield safety guarantees for a wide spectrum of uncertainty types. This leads to
controllers that enforce robust safety guarantees while their conservativeness
scales by the parameterization. To illustrate the generality of this approach,
we show that input-to-state safety (ISSf) is a special case of the PBF
framework, whereby improved safety guarantees can be given relative to ISSf.
