This is a controversial topic, widely misunderstood outside the ranks of Islamic art historians, who are familiar with the "preponderance" of figurative art that contradicts the assumption that "Islamic" art excluded representations of living beings (quote is from Grabar, Masterpieces, cited below, p. 19). Hence I supply a few references. For Ottoman figural imagery, specifically Sultanic portraiture, its antecedants in Ilkhanid art with relevant Chinese conventions, and comparisons to Mughal and Safavid painting, see:
Gülru Necipoğlu, "Word and Image: The Serial Portraits of Ottoman Sultans in Comparative Perspective," in Selmin Kangal, ed., The Sultan's Portrait: Picturing the House of Osman. (Istanbul 2000).
For a general and authoritative overview of the nature of early Islamic art:
Oleg Grabar, The Formation of Islamic Art (Yale University Press, 1973, revised 1987).
For an accessible collection with many beautiful examples of figurative images from Islamic manuscripts:
Oleg Grabar, Masterpieces of Islamic Art: The Decorated Page from the 8th to the 17th Century. (Prestel, 2009). See pp. 30, 60, 138 for pictures of Ottoman sultans in Topaki Palace collection. Pp. 18-31 provides brief introduction that sets Ottoman painting in its historical context.
The licit status of figural art varied across time as well as space in Islamic civilization. For a nice example of licit becoming illicit in the transmission of images of Ottoman sultans:
Finbarr Barry Flood,"Lost Histories of a Licit Figural Art," International Journal of Middle East Studies 45 (2013).
The variable licit status in the medieval and early-modern era does not align with the Sunni/Shi'a division, even for the most vexed issue--figural figural images of Muhammad. For a survey of this in early Islamic art, with comments on some contemporary practices:
Christiane Gruber, "Between Logos (Kalima) and Light (Nūr): Representations of the Prophet Muhammad in Islamic Painting." In Muqarnas: An Annual on the Visual Culture of the Islamic World 26 (2009).