Projection system, method of controlling projector, and projector

A projection system includes a recursive reflector located in a first area of a projection surface, a projection device configured to project a first image and a second image at respective timings different from each other, an imaging device configured to image a first projection area in a situation in which the projection device projects the first image in the first projection area including the first area to thereby generate imaging data, and a control device configured to identify a position of the recursive reflector based on the imaging data, and decide a second projection area in which the second image is projected based on the position of the recursive reflector, wherein the projection device and the imaging device are disposed so that a contrast ratio between the recursive reflector and a periphery of the recursive reflector becomes equal to or higher than a predetermined value.