A drive system includes an engine as a drive source, a lead storage battery that is charged using the engine as a motive power source, a starter that starts up the engine by being driven by electric power from the lead storage battery, and a battery sensor that measures an inter-terminal voltage of the lead storage battery. A control device that is applied to the drive system temporarily stops the engine when a temporary stop condition is satisfied, and starts up the engine again when a discharge amount of the lead storage battery in a period of the temporary stop is larger than a discharge upper limit amount. When an inrush voltage is equal to or lower than a restraint threshold, the discharge upper limit amount is set so as to be smaller than when the inrush voltage is higher than the restraint threshold.