Emotional control is a traditional element of martial arts training. From a practical POV it's an important part of training because one needs to keep one's head relatively cool under extreme fear and pressure during a real fight. Without emotional training it's becomes very difficult for someone to put their training into practice.

There have been studies into this - one particular interesting study was conducted by Darren Laur in his article "The Anatomy of Fear and How It Relates to Survival Skills Training." Laur himself is a serving law enforcement professional and some of his research was conducted with riot police training.

Anyway, you can follow that link and read it in more detail for yourself, but to put it simply:
+ You WILL experience fear in a fight. Your metabolic rate increases under fear, which Laur measures according to heartrate (beats per minute - bpm) - in a fight a person's heartrate can change from 70bpm to 220bpm in less than half a second.
+ At 115bpm fine motor skills are diminished, but your gross motor skills are heightened. Thus the optimum performance range for fighting is between 115-145bpm.
+ Once you exceed 145bpm most people will lose complex motor skills and may suffer things like diminished hearing, peripheral narrowing (tunnel vision), memory loss, disassociation (a sense of detachment from reality), intrusive distracting thoughts, memory distortion -- and in some individuals, even temporary paralysis. Beyond this level some individuals may even urinate and/or defecate themselves as the body automatically engages in "losing ballist" to make your body lighter for a faster escape.
+ At 185-220bpm most people go into a state of "hypervigilance" or "deer in the headlights" mode where they simply freeze up or engage in irrational behaviour like going into danger (this is because the brain goes into some kind of feedback loop).

Thus emotional training is important to teach students to remain focused and optimised in order to use their skills in self defence. You cannot ignore your fear - you have to accept the fact that you WILL be frightened like all bugger in a fight. But emotional training teaches you how to work with your fear - not against it; after all, fear has some advantages in a fight, like the optimisation of gross motor skills. Some people experience heightened visual clarity and "slow motion" time (ever fallen off your bicycle and felt like time was slowing down? It's because your brain is actually thinking faster, hence why time seems to go slower - again a natural defensive reaction).

There are lots of training techniques that can be employed to ensure that self defence skills can work in a frightening survival situation, and the article explains them in detail. One time-honoured practice is autogenic breathing. Studies have shown that autogenic breathing can decrease one's heart rate up to 30% for up to 40 seconds. So if a person's heartrate was sitting at 175-220bpm, autogenic breathing can reduce it to 115-145bpm, which is the optimum range for combat effectiveness. So as you can see, all that Zen meditation stuff that martial artists practice actually do serve a practical purpose.

Anyway, check out Laur's article as it does document the research in thorough detail.