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Constant-power (CP) loads alter the conventional dynamic analysis of dc-dc converters. This paper examines boundary control strategies for dc-dc buck converters subject to constant-power loads. Boundary control addresses global system behavior and avoids the limitations of linearization. Converter dynamics is analyzed in both switching states and the various operating regions of switch interaction with a first-order switching surface (boundary) are identified. Sufficient conditions for large-signal stability of the closed loop system are established. It is also shown that in this application, instability as well as system-stalling, which we term the invariant-set problem, may still occur in reflective mode. Design considerations are included and recommendations are given. The theoretical analysis is verified by simulations and experimental results.