Confusion about Thevenin's theorem for linear circuits with non-linear elements
As your quotation says, linear power supplies are called linear because of the transistor's (BJT's) operating region, not because it's a linear circuit.

To find a Thevenin equivalent for a nonlinear circuit, you can do the same things you do for any transistor amplifier:


Make the AC components of the input conditions small.
Use a nonlinear, large-signal model to find the characteristics of the circuit at the DC bias point.
Make a linearizing approximation around the bias point (a so-called "small-signal model").
Plug your small AC signal into the small-signal model to get the AC output.


The typical small-signal model for BJTs is the hybrid-pi model. So starting with a linear regulator:







simulate this circuit &ndash; Schematic created using CircuitLab

You would end up with this:







simulate this circuit

That's a linear circuit, so it has a Thevenin equivalent. This model only applies when changes in the voltages and currents are small, though. That's the price you pay for linearity.

You can't do this directly with an SMPS -- the switching can't be linearized.  For a constant duty cycle, you can use a transformer to model the switching action. In the comments, Tom mentions a source for linearizing the control loop.