  This letter presents a new notion of input-to-state safe control barrier
functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under
input disturbances. Similar to how safety conditions are specified in terms of
forward invariance of a set, input-to-state safety (ISSf) conditions are
specified in terms of forward invariance of a slightly larger set. In this
context, invariance of the larger set implies that the states stay either
inside or very close to the smaller safe set; and this closeness is bounded by
the magnitude of the disturbances. The main contribution of the letter is the
methodology used for obtaining a valid ISSf-CBF, given a control barrier
function (CBF). The associated universal control law will also be provided.
Towards the end, we will study unified quadratic programs (QPs) that combine
control Lyapunov functions (CLFs) and ISSf-CBFs in order to obtain a single
control law that ensures both safety and stability in systems with input
disturbances.
