  This paper proposes control approaches for discrete-time linear systems
subject to stochastic disturbances. It employs Kalman filter to estimate the
mean and covariance of the state propagation, and the worst-case conditional
value-at-risk (CVaR) to quantify the tail risk using the estimated mean and
covariance. The quantified risk is then integrated into a control barrier
function (CBF) to derive constraints for controller synthesis, addressing tail
risks near safe set boundaries. Two optimization-based control methods are
presented using the obtained constraints for half-space and ellipsoidal safe
sets, respectively. The effectiveness of the obtained results is demonstrated
using numerical simulations.
