  This paper studies the problem of safe control of sampled-data systems under
bounded disturbance and measurement errors with piecewise-constant controllers.
To achieve this, we first propose the High-Order Doubly Robust Control Barrier
Function (HO-DRCBF) for continuous-time systems where the safety enforcing
constraint is of relative degree 1 or higher. We then extend this formulation
to sampled-data systems with piecewise-constant controllers by bounding the
evolution of the system state over the sampling period given a state estimate
at the beginning of the sampling period. We demonstrate the proposed approach
on a kinematic obstacle avoidance problem for wheeled robots using a unicycle
model. We verify that with the proposed approach, the system does not violate
the safety constraints in the presence of bounded disturbance and measurement
errors.
