  In a complex real-time operating environment, external disturbances and
uncertainties adversely affect the safety, stability, and performance of
dynamical systems. This paper presents a robust stabilizing safety-critical
controller synthesis framework with control Lyapunov functions (CLFs) and
control barrier functions (CBFs) in the presence of disturbance. A high-gain
input observer method is adapted to estimate the time-varying unmodelled
dynamics of the CBF with an error bound using the first-order time derivative
of the CBF. This approach leads to an easily tunable low order disturbance
estimator structure with a design parameter as it utilizes only the CBF
constraint. The estimated unknown input and associated error bound are used to
ensure robust safety and exponential stability by formulating a CLF-CBF
quadratic program. The proposed method is applicable to both relative degree
one and higher relative degree CBF constraints. The efficacy of the proposed
approach is demonstrated using a numerical simulations of an adaptive cruise
control system and a Segway platform with an external disturbance.
