In this paper, the problem of the output voltage regulation of buck converters is considered.The novelty of the problem statement is that the external electric load and the input voltage of the converter are unknown bounded functions of a certain class. In particular, the external load equivalent scheme is similar to the successive connection of the inductive and resistive elements. In this case, the behavior of the load current is described by the differential equation with time-varying coefficients. In this equation, the equivalent inductance and resistance are described by unknown arbitrary bounded functions with several bounded derivatives. Under known bounds for these functions and their derivatives, the initial system can be transformed into the special form with smooth bounded perturbation. This disturbance is an unknown function, and its action channel differs from the input channel. Therefore, the influence on the unknown external load can not be compensated for directly by the control input. Due to this reason, the new control strategy is developed in the paper with the help of a “vortex” algorithm, which provides asymptotic convergence of the regulation error to zero in time. How to choose the converter parameters and the bounds for the input voltage to operate the closed-loop system properly are shown. The convergence proof is organized with the help of the Lyapunov function approach, and the transient rate is also estimated. The simulation results show the efficiency of the designed control law for the wide class of input voltage and electrical parameter functions. The proposed control scheme may be further used in electric drive systems.