I have attached photo of a lecture where a slide is showing a close loop control system(theif repulsion system). But i am confused by the electric eye?how it is working?is the robber/theif so mad that he is carrying an IR source in his hand?(normally a theif is expected to have a pistol or knife in his hand)
The electric eye, in this case, is a PIR sensor (Passive infrared sensor). These type of sensors detect the movement of objects that emit IR radiation. IR radiation is also called heat radiation, and every human emits heat. That's why the "electric eye" in your case detects a thief. The thief does not have any external IR source, he is the actual IR source himself!
You can check a Wiki page for PIRs for more info. Also, there are great videos on YT for a better explanation if you need it: https://en.wikipedia.org/wiki/Passive_infrared_sensor
Haris Basaric's answer is correct, but you should be aware that the example shown is NOT a closed-loop system. It is an open-loop system.
The burglar gets close to the sensor, and the sensor turns on the lights. By itself, this does not affect the input.
The underlying assumption (not stated) is that turning the lights on will cause the burglar to run away, removing the IR from the sensor and turning the lights back off. While this is generally a reasonable assumption, it is not guaranteed. Until you CAN guarantee it, the system as shown is not closed-loop.
If the slide stated, "The burglar then runs away, causing the input to return to normal", or something like that, the slide would be OK.
Beware of unstated assumptions.