"What defines “contemporary art music”?"
Music that engages the listener beyond the expected and breaking new ground with innovation and passion for which can only be described as amazing. Often this music introduces new instruments or new techniques for traditional instruments as well as presenting traditional instruments in new ways, e.g. John Cage prepared piano. This music may challenge any of the traditional foundations of melody, harmony, rhythm, texture, structure, dynamics, notation, timbre, length, size, and shape while perfectly standing on its own.
This area of music is like a nebula preparing to give birth to a galaxy, a stellar nursery, but there is nothing childish or infantile about it. What some may call experimental, those who understand it will tell you it is beyond the lab and ready for ingestion. In short, a way of making the obscure clear and the unstable profoundly substantial.
"I would greatly appreciate some suggestions on current contemporary art composers and music."
Here is my short list of contemporary art music composers of the last 25 years. No special order, and my apologies to the ones I omitted to keep this short.
Robert Ashley: Many operas for television including "Celestial Excursions" (2003)
David Behrman: "My Dear Siegfried" XI Records, 2005 and many other electronic pieces.
John Adams: "On the Transmigration of Souls" (2002), a choral piece commemorating the victims of the September 11, 2001 attacks (for which he won a Pulitzer Prize in 2003) and many other amazing works including operas:
>>> more than 25 years ago but well known <<< (1987) Nixon in China
(1991) The Death of Klinghoffer
(1995) I Was Looking at the Ceiling and Then I Saw the Sky
(2000) El Niño (opera-oratorio)
(2005) Doctor Atomic
(2006) A Flowering Tree
(2012) The Gospel According to the Other Mary (opera-oratorio)
Meredith Monk: A recipient of the MacArthur Fellowship. Her recent works include "Possible Sky" for orchestra and voices (commissioned by Michael Tilson Thomas for the New World Symphony, 2003) and "Stringsongs" for string quartet (commissioned by the Kronos Quartet, 2004).
John Luther Adams: 2014 Pulitzer Prize in Music for his composition "Become Ocean".
Philip Glass: Three of his film scores have been nominated for Academy Awards.
Terry Riley: 2008: "Banana Humberto", piano concerto with Paul Dresher Ensemble and many other great works.
Steve Reich: 2009 Pulitzer Prize, “Double Sextet" and many other wonderful works.
Rhys Chatham: He is best known for his guitar orchestra compositions, "A Secret Rose" (for 100 electric guitars) and "A Crimson Grail For 200 Electric Guitars" performed live at Lincoln Center Out of Doors in New York City, August, 2009.
Please search Google and Youtube for each of these composers so you can see and hear their works performed. This represents a wide range of what is going on in new music so I am hopeful you'll find a piece worthy of your analysis.
Also, you might want to review all the Pulitzer Prizes for composition in the last 25 years, MacArthur Foundation awards, and other prestigious awards in this field for other interesting and worthy composers.