In Wikipedia, you can find the definition of the inertial frame of reference, which states:
In classical physics and special relativity, an inertial frame of reference (also inertial reference frame or inertial frame, Galilean reference frame or inertial space) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner.
Actually, I don't think it's a good definition or a good description. So just like we define the equilibrium state in thermodynamics, can we propose a similar definition by comparison? I mean can we take three reference systems with different constant velocities and make a comparison between the corresponding state of motion and then give the definition of the inertial frame of reference?