  This paper introduces integral control barrier functions (I-CBFs) as a means
to enable the safety-critical integral control of nonlinear systems.
Importantly, I-CBFs allow for the holistic encoding of both state constraints
and input bounds in a single framework. We demonstrate this by applying them to
a dynamically defined tracking controller, thereby enforcing safety in state
and input through a minimally invasive I-CBF controller framed as a quadratic
program.
