An Imperial-class Star Destroyer served in Darth Vader's Imperial Death Squadron, a specialized group under the command of the Sith Lord assembled to locate the Rebel Alliance's headquarters, after the Hoth campaign in 3 ABY. A captain was in command of the Star Destroyer. The Star Destroyer's bridge was struck by a sizable asteroid during the search for the Millennium Falcon within the Hoth asteroid field, leading to the destruction of the warship.
This specific Star Destroyer, under the command of an unidentified captain, was part of Darth Vader's Death Squadron. This fleet, the personal command of the Sith Lord, was tasked with locating the base of operations for the Rebel Alliance following the Battle of Hoth.
After Han Solo escaped Echo Base on Hoth with his Wookiee co-pilot Chewbacca, Princess Leia Organa, and the protocol droid C-3PO aboard his freighter, the Millennium Falcon, he sought refuge in the nearby Hoth asteroid field to evade the pursuing Imperial Navy. In an attempt to seize the freighter, Vader dispatched numerous Star Destroyers, including this one, the Star Dreadnought Executor, and the Avenger, into the chaotic asteroids in order to force the Millennium Falcon and its occupants out of hiding and into the control of the Empire.
The captain of this Star Destroyer participated in a holographic meeting with nineteen other battleship commanders, including Captain Lorth Needa of the Avenger, alongside Vader on the Executor, to discuss the status of the elusive Millennium Falcon. During this conference, a massive asteroid struck the bridge tower of this Star Destroyer, resulting in the warship's complete destruction.
This Star Destroyer, along with its captain, made its first appearance in the 1980 novelization of Star Wars: Episode V The Empire Strikes Back. While its destruction is not explicitly shown in the film, the novelization and the junior novelization clearly state that the warship was destroyed by the collision. The destruction of this ship, along with another unidentified Star Destroyer, is depicted in Star Wars (1977) 42.