TRACON Controller reported an aircraft with a stuck transmitter temporarily lost control and descended below the terrain minimums and towards an obstruction.

Narrative

Aircraft X had a stuck mic trying to transition through our airspace at 080. We advised him of the situation and he proceeded with losing control of his aircraft and not following his clearance. He decided his equipment was malfunctioning and asked for vectors to ZZZ. I; the Radar Controller for the ZZZ airspace; vectored him and gave him instructions to only acknowledge with an ident since his equipment radio was not working. I gave him all appropriate weather information and the NOTAMs for the airport.During his initial visual approach I did not have good faith he was heading for the airport and he was going toward a tower light obstruction. I decided to give a low altitude alert and instructed him to climb and maintain 030. The second time around for the visual approach; I coordinated with the Tower Controller to turn the lights up on the field and give light gun signals to the aircraft. I also instructed the aircraft he was cleared to land Runway XX short end. Then; I handed him off to the Tower frequency and he eventually landed safely at ZZZ.Aircraft X needs to fix his aircraft equipment.