Thirupalliyezhuchi was composed by Thondaradippodi Alvar, who lived in 8th century of CE in Thirumandangudi, Tamil Nadu.
Songs for waking up the Lord was not a common tradition in Hinduism. The famous exhortation of Sage Viswamithra to Lord Rama in Bala Kanda of Valmiki Ramayana viz
Kousalya Supraja Rama, Poorva Sandhya pravarthathe, Uthishta Nara Sardula , Karthavyam daivamahnikamWhich requested him to wake up and do his ritualistic duties to God, is perhaps the only such waking up poem of the Puranas. This is strange since the system of sending Lord to sleep and waking up is prevalent in most of the famous temples of Tamil Nadu. This great Suprabhatam (called Thiru palli ezhuchi) to wake up Lord Ranganatha which belongs to the Vaishavite literature or the one by Manikkavasagar to wake up lord Thiruperum thurai near trichinopoly which belongs to the Shaivite literature must be one of the first Suprabathams ever written. This Ranganatha Suprabhatam is chanted in all Vaishnavism temples of south india including Thirupathi in the month of Mārkazhi (Mārgaṣīrṣa). Sri Venkatesa Suprabatham which is used to wake up Lord Venkateswara of Thirupathi which was written about a hundred years back must be the most popular one.