Theorems on hyperexponential stability are proposed for both explicitly and implicitly defined Lyapunov functions. It is shown that finite-time and fixed-time controls based on the use of implicitly defined Lyapunov function provide hyperexponential stability under sampled-time realization. A rated hyperexponential control is proposed for linear systems. Preliminary numerical experiments show that the proposed control law is less sensitive to measurement noise and has better performance under input delays compared to finite-time analogs.