This paper proposes a distributed strategy regulated on a subset of individual buses in a power network described by the swing equations to achieve transient frequency control while preserving asymptotic stability. Transient frequency control refers to the ability to maintain the transient frequency of each bus of interest in a given safe region, provided (i) it is initially in it, and (ii) if it is initially not, then drive the frequency to converge to this region within a finite time, with a guaranteed convergence rate. Building on Lyapunov stability and set invariance theory, we formulate the stability and the transient frequency requirements as two separate constraints for the control input. Our design synthesizes a controller that satisfies both constraints simultaneously. The controller is distributed and Lipschitz, guaranteeing the existence and uniqueness of the trajectories of the closed-loop system. We further bound its magnitude and demonstrate its robustness against measurement inaccuracies. Simulations on the IEEE 39-bus power network illustrate our results. (C) 2019 Elsevier Ltd. All rights reserved.