A second person familiar with the probe said investigators were looking at how the pilots dealt with the chain of events leading up to the crash. Neither person agreed to be identified, because details of the investigation remain confidential.
The pair of computers comprising the A320's FAC system is mainly responsible for controlling rudder movements and helping to keep the airplane stable, as well detecting windshear, or sudden changes in wind speed or direction.
Indonesian magazine Tempo reported a series of maintenance problems with the computerized rudder system of that particular aircraft in the days and months before the loss of Flight QZ8501.
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Pictures of wreckage retrieved from the Java Sea provide little evidence that the crash was caused by problems with the rudder.
But, after partially analyzing data from the "black box" voice and flight data recorders, investigators have extended their interest to the FAC computers, the two people familiar with the probe said.
A problem with the system may help explain another key element of the crash - why the jet did not automatically correct itself before entering into a stall, even if accidentally encouraged to do so by crew.
Airbus jets are designed to provide "flight envelope protection", making it virtually impossible to push them outside safe design limits when operating in normal flying mode.
But when the computers are unable to perform their tasks, control is automatically handed to the pilots who must fall back on training and fly manually, in so-called "alternate" mode.
A failure of both FAC computers - one primary, the other back-up - is one of those rare circumstances that can cause the usual stall protection to trip.
That alone would not explain why such a jet might crash and it is unlikely to be the only scenario being considered by investigators.
It was not clear when any fault might have developed, but it would, if confirmed, be one possible explanation of how the plane got into the state where the Indonesian pilot and French first officer would need to take over and display skill under stress.
"Stall protection can trip in very exceptional circumstances and the pilots need to react to that," an A320 pilot said, asking not to be named since he is not allowed to talk to media.
Airbus said it would not comment on the investigation or the crashed jet, but stressed that this type of aircraft is designed to be flown manually even when the safety buffer is not available.
"The aircraft remains fully controllable if you lose the two FACs," an Airbus spokesman said by email.