We report two ultra-stable laser systems automatically frequency-stabilized to two high-finesse optical cavities. By employing analog-digital hybrid proportional integral derivative (PID) controllers, we keep the merits of wide servo bandwidth and servo accuracy by using analog circuits for the PID controller, and, at the same time, we realize automatic laser frequency locking by introducing digital logic into the PID controller. The lasers can be automatically frequency-stabilized to their reference cavities, and it can be relocked in 0.3 s when interruption happens, i.e., blocking and unblocking the laser light. These automatic frequency-stabilized lasers are measured to have a frequency instability of 6×10-16 at 1 s averaging time and a most probable linewidth of 0.3 Hz. The laser systems were tested for continuous operation over 11 days. Such ultra-stable laser systems in long-term robust operation will be beneficial to the applications of optical atomic clocks and precision measurement based on frequency-stabilized lasers.