Located at a distance of roughly 880 light years (270 pc) [1, 2], DI Pegasi was identified in 1934 an Algol-type binary star system [3]. This class of star systems, which is named after the star system Algol, consists of two stars, one of which is brighter and hotter than the other but has a smaller diameter. In the DI Pegasi system specifically, the brighter star is a Sun-like hydrogen-burning star with a mass of 1.19 times the mass of the Sun, and the fainter star is a larger red giant with a mass 0.70 times the mass of the Sun [4]. The two stars orbit each other very closely; they are separated by a distance that is equivalent to about 4.1 times the radius of the Sun [5]. In our Solar System, this would be equivalent to placing a small red giant inside Mercury's orbit and having extra room to spare. The orbits of the two star are aligned in such a way that, as seen from Earth, each star will eclipse the other star, with the biggest change in brightness occurring when the bigger but fainter red giant passes in front of the smaller but brighter Sun-like star.
One of the unusual things about Algol-type variable star systems is that the less massive star is the red giant [6]. In general, when two or more stars form at the same time, as would be the case in these types of systems, the more massive stars are expected to become red giants before less massive stars, so it seems unusual that the less massive star in any Algol-type star system is a red giant. The simple explanation for why these binary star systems look this way is that the less massive red giant was originally the more massive star, but when it originally expanded to become a red giant, it got so large that the smaller star was able to gravitationally strip away its outer gas layer, thus making the red giant smaller in both diameter and mass [5]. So, problem solved.
DI Pegasi, however, had an additional problem. For a few decades, people have seen variations in the orbital periods of the two stars. The orbital period was originally measured in 1934 as 17 hours and 5 minutes [7], but it has been seen to vary by plus or minus 15 minutes since then [4, 5]. People eventually figured out that the apparent variation in the orbital period was caused by the presence of two more stars in the system that were orbiting relatively far away but that were gravitationally interacting with the central two stars.
Based on decades of observations, astronomers have been able to derive a little bit of information about these other two stars. One star has a mass of about 0.095 times the mass of the Sun, which makes it a very small red dwarf with just enough mass to still trigger the fusion of hydrogen into helium in it core [4]. It orbits the system once every 23 years [4], and its favorite Pokemon are Jigglypuff and Vulpix. The other star is a larger red dwarf with a mass of 0.170 times the mass of the Sun [4]. It completes an orbit one every 54.6 years [4], its favorite dessert is pineapple upside down cake (which I personally don't like), and it prefers a window seat instead of an aisle seat.
Anyway, as these two red dwarfs orbit the two bigger stars at the center of the system, they will gravitationally pull on the central pair of stars, causing them and their center of gravity to slowly move towards and away from the Earth. As the two central stars approach the Earth, the time in which it takes light to reach the Earth decreases a little between each eclipse, which in turn makes the period in which the stars eclipse each other also appear to decrease. Similarly, when the central pair of stars is moving away from the Earth, the time in which light takes to reach the Earth between eclipses will increase, and this will make the period of variability also appear to increase a little over time. It's sort of related to Doppler shifting but it's also not quite the same phenomenon. We are not talking about stretching out or squeezing waves of light, which is what Doppler shifting is, but we are looking at stretching out or squeezing the observed length of the time period between when we see the stars eclipse each other.
DI Pegasi is not the only multiple star system with a pair of eclipsing stars where this type of phenonenon is seen, but it does seem to be a really good example of it, and I would expect that it could be used in future surveys that study the diversity of multiple star systems within our galaxy.