"A true-born martinet never thinks he is at all severe."
Poor Nellie(1888)

Martinet pronounced (mar-t(ê)n-'et) is an eponym. As Webby 1913 notes it means a strict disciplinarian or one who demands absolute adherence to forms and rules. The word martinet was around and in use by the French long before it became infamous. During the fourteenth century it appeared as the name of two birds, the martin, as well as, the swift. Then a chandelier, and by 1743 it was used to identify a whip used on children, It was also a word that named the demon who called forth the witches to their assemblies. Perhaps it stuck in todays lexicon because during the medieval days it was the name of military engine that catapulted large stones.

The noun today is credited primarily to a 17th century French army officer by the name of Jean Martinet (?-1672). He served under Louis XIV during the Dutch campaign. Well known for as a tactician and as a military engineer he created many forms of battle strategies, built a copper assault boat and devised pontoon bridges. He was known to go to the extreme of ordering executions for even minor infractions. Because of that his name came to be synonymous with the severity of discipline. A lieutenant colonel in the Régiment du Roi in 1670 he added a grenadier company and is credited in part for transforming the French Army from an armed mob, into a somewhat effective fighting force. By somewhat effective I mean he was shot "accidentally on purpose" by his own men during the Battle of Duisburg; inadvertently killed when he entered the line of fire of his own rear ranks. Perhaps one of the men in his unit had simply had more than his fair share Martinet's strict training methods. In any event, his name lives on today, in senses that extend well beyond military discipline.

Sources:

inter alia:
http://lhostelaw.com/

Jean Martinet:
www.biography.com/

Vive le Roi! Vive l'Empéreur!:
pages.prodigy.net/

yourdictionary:
http://www.yourdictionary.com