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An important issue in the trends of miniaturization of systems-on-chips (SoCs) is to obtain a high energy efficiency. This can be reached by dynamic voltage scaling (DVS) architectures as the novel discrete Vdd-Hopping circuit. Generally, this kind of systems present parameter uncertainties and delays. Likewise, current peaks and energy dissipation must be reduced. In this paper, an optimal and robust saturated control law is proposed for this Vdd-Hopping circuit via Lyapunov-Krasovskii theory that ensures asymptotic stability as well as system robustness with respect to delay presence and parameter uncertainties. The closed-loop system presents a regional stabilization due to the actuator saturation. An estimation of an attraction domain is provided. This controller also limits the current peaks and it provides an energy-aware performance. The advantages achieved with this controller are shown in simulation.