Soft-start circuitry is designed to minimize inrush current and decrease the stress on power elements at power up. It is implemented by ramping the internal reference of the error amplifier. In some devices this can be accomplished simply with an RC circuitry, in other cases the solution is more sophisticated like the one shown on the slide. This is relevant to the L598x series of step down regulators: the reference ramps up as a staircase made up of 64 steps, 9 mV per step (the final voltage is 0.6 V) and each step duration is 32 clock cycles. This means the actual soft-start time depends on the switching frequency, according to the formula shown. The output voltage follows the reference voltage, it will ramp up accordingly, with the same slew rate.