A method for controlling a display device having a first interface to which a first image signal is inputted and a second interface to which a second image signal is inputted from an image supply device having an auto sleep function is provided. The method includes: shifting to a sleep mode in response to a continuous stop of the first image signal for a first time, in a first mode in which a first image based on the first image signal is displayed on a screen; and shifting to the sleep mode in response to a continuous stop of the second image signal for a second time that is shorter than the first time, in a second mode in which a second image based on the second image signal is displayed on the screen.