it's not a complete sentence. but also not just three seperate words. it's a conjuction, a noun phrase joint. this joint of phrase is used in persian language so turks use it their literature as their type of phrase joint. it means about "nation of eternal duration". this is not the exact translation of course but similar at least.
yes, it's Turkish. of course each of the words in the phrase is Arabic in root. but gramatic of the phrase is not Arabic. that's Persian. "devlet-i ebed müddet". and its usage has a place in Turkish literature. it means "infinit state" or something like this.
which means that the original phrase is not arabic, its true, each word sounds arabic, but together they mean nothing...
Dawlat (wrong spelling as well) means country or state
Abad: Ever or eternity
Maddat: stretched or extended
but they dont work together