Frequency stabilized light sources with narrow linewidth are mandatory for atom interferometry based experiments. For compact experiment designs used on space platforms, tunable DFB diode lasers are often used. These lasers combine low energy consumption with small sizes, but lack long-term frequency stability. This paper presents an FPGA based laser frequency stabilization system for highly variable target frequencies using frequency modulated Rb-spectroscopy achieving latencies below 100 μs. The system consists of a DFB laser, a Rb-spectroscopy cell, a laser current controller and an FPGA board with an analog-digital conversion board. The digital part of the frequency stabilization system is a SoC mapped on an FPGA. The SoC consists of a processor, enabling user interaction via network connection, and the dedicated frequency stabilization module. This module consists of a demodulation stage, digital filters, a frequency estimator and a controller. To estimate the frequency, small ramps of the laser frequency are generated using a high-speed DAC connected to the laser current controller. The absorption spectroscopy output of this beam is sampled using a photodiode and a high-speed ADC. After signal conditioning with digital filters, the frequency estimator extracts the present mid-frequency of the laser applying pattern matching with a prerecorded reference spectrum. The frequency controller adjusts the mean laser current based on this estimation. The performance as well as the accuracy of the proposed laser stabilization system and its FPGA resource and power consumption are evaluated.