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This paper addresses the problem of time-optimal load-transient response in digitally controlled dc-dc buck converters incorporating an inductor current limitation. The concept of current-limited, time-optimal control (CL-TOC) is introduced and compared to the conventional unconstrained time-optimal solution. A fundamental tradeoff between maximum-allowed current overshoot and voltage recovery time is recognized and analytically formulated, thus providing the engineer with the necessary analytical tools for performance evaluation. Furthermore, the minimum number of switching actions required to handle a generic CL-TOC transient is determined, thus leading to the formulation of a minimum-switch CL-TOC concept. Two distinct approaches for implementing minimum-switch digital CL-TOC are then introduced. The first method extends a parameter-independent time-optimal control that has the advantage of achieving the time-optimal switching sequence without the need for a prior knowledge of the output filter LC parameters or input voltage. The second approach implements a near CL-TOC employing the switching-surface concept and defining the current limitation in the state space. Experimental results are provided to validate the theory and demonstrate the effectiveness of the approaches.