The problem of finite-time stabilization of linear systems under state and control input constraints in the presence of external disturbances is addressed. The proposed control is designed such that the closed-loop system is 1) superstable, when system trajectories risk to violate the state constraints, and 2) homogeneous with a negative degree, otherwise. While the former property ensures the fulfillment of the state and control constraints, the latter implies finite-time stability. The robustness of the control scheme with respect to disturbances is studied. Theoretical results are supported by numerical simulations.