A simple test we've often utilized in both time domain simulations and actual physical hardware is based upon a Dirac Doublet Impulse which has zero average value, thus doesn't upset the DC bias conditions when "injected" into a system.
In simulations the doublet is created with a simple current PWL source with start at 0, then Ipeak, then -Ipeak, then 0. Select the amplitude and time spacing to ones system speed needs. This can be "injected" anywhere in the system to evaluate stability by means of evaluating the time domain impulse response.
For hardware use we originally developed this back in ~1970s and called it the "Pinger", where the doublet was created by a 555 timer, some high speed logic for a variable rate and impulse width spacing, then differentiated with a small series cap to a pot for level settings with a series R to the Pinger tip. We used the old aluminum Probe "cans" from Heathkit (recall) to house the "Pinger". Later we made some CMOS versions, worked really well and quickly allowed system stability tests & verification for different conditions.
Anyway, someday we may resurrect the "Pinger" if it hasn't already been done by others.
Best,