MILAN,— Giorgio Armani, the Italian designer who transformed modern fashion and became one of the most recognized names in luxury clothing, has died at 91, his company said Thursday. Armani, founder of the Armani Group and the creative force behind the brand for nearly half a century, passed away after a period of illness, according to a statement released by the fashion house. “With deep sadness, the Armani Group announces the death of its founder, creator and driving force: Giorgio Armani,” the company said. His passing comes as the group was preparing to celebrate its 50th anniversary this month with an exhibition during Milan Fashion Week. Often called “Re Giorgio,” or King Giorgio, Armani leaves behind a global fashion empire, a distinctive minimalist style, and a reputation as one of Italy’s most enduring cultural icons.