Why does the time-domain mathematical model of linear time-invariant system remain unchanged?
Because linearity is time-invariant. Linear time-invariant system means that the parameters of the system do not change with time, that is, regardless of the time sequence of the input signal, the shape of the output signal response is the same, but the time of appearance is different. The time-domain mathematical model of linear time-invariant system is invariant, because it is linear time-invariant, a general mathematical model and the most general description of linear time-invariant system.