Actually Musicnoise, I think the origin of the term "damping factor" for audio amplifiers has much humbler roots than classical Control Theory.
In these days of direct-coupled amps, it makes sense to specify output impedance, but when virtually all audio amplifiers had multiple output taps . . . I can see where it may have been handy to express this as a single, approximate number for all output impedance configurations.
And differences in the amplifier output impedance can logically be likened to differences in the amount of stuffing inside a speaker box . . . or the compliance in a speaker cone . . . and if we call this "speaker damping", then "damping factor" for an amplifier is actually pretty concise and specific, especially in the world of published consumer electronics specifications. Just a bit anachronistic today.
In these days of direct-coupled amps, it makes sense to specify output impedance, but when virtually all audio amplifiers had multiple output taps . . . I can see where it may have been handy to express this as a single, approximate number for all output impedance configurations.
And differences in the amplifier output impedance can logically be likened to differences in the amount of stuffing inside a speaker box . . . or the compliance in a speaker cone . . . and if we call this "speaker damping", then "damping factor" for an amplifier is actually pretty concise and specific, especially in the world of published consumer electronics specifications. Just a bit anachronistic today.