  This paper presents a framework for designing provably safe feedback
controllers for sampled-data control affine systems with measurement and
actuation uncertainties. Based on the interval Taylor model of nonlinear
functions, a sampled-data control barrier function (CBF) condition is proposed
which ensures the forward invariance of a safe set for sampled-data systems.
Reachable set overapproximation and Lasserre's hierarchy of polynomial
optimization are used for finding the margin term in the sampled-data CBF
condition. Sufficient conditions for a safe controller in the presence of
measurement and actuation uncertainties are proposed, for CBFs with relative
degree 1 and higher relative degree individually. The effectiveness of the
proposed method is illustrated by two numerical examples and an experimental
example that implements the proposed controller on the Crazyflie quadcopter in
real-time.
