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This paper analyzes the general problem of inductor current limitation in the time-optimal load transient response of a DC-DC buck converter. The concept of current-limited, time-optimal control (CL-TOC) is introduced and compared to the previously reported unconstrained time-optimal solutions. A fundamental tradeoff between maximum allowed current overshoot and voltage recovery time is recognized, and a set of design equations is developed which provide the engineer with the necessary analytical tools for the controller design. Furthermore, the minimum number of switching actions required to handle a generic current-limited TOC is determined, leading to the formulation of a minimum-switch CL-TOC concept. Two distinct approaches for minimum-switch digital CL-TOC are then introduced. The first method, which is an extension of a charge-balance approach, has the advantage of achieving the time-optimal switching sequence without the need for a prior knowledge of the output filter LC parameters. The second approach implements a near CL-TOC employing the switching surface concept and defining the current limitation in the state-space. Simulation and experimental results are provided to demonstrate the effectiveness of the approaches.