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Conditional stability
It is true that a system with > 180 deg. phase shift at some low frequency behaves nicely and is completely stable, provided that the phase shift gets back well below 180 degrees at the crossover frequency. To the human mind  at least mine  it seems very strange why such a system does not oscillate violently, but the math shows it, and so does reality.
Some designers like to put two amplifiers with infinite DC gain in series in their feedback path, believing that two must be better than one. This is one way to create a conditionally stable system. It is perfectly stable but may also be found in a state of violent self oscillation. Once it has become unstable, it is unable to recover by itself.
What happens is that the oscillating system has a much lower effective open loop gain than normal, due to clipping of the signal in some of the amplifiers. A large reduction of effective gain is just what a conditionally stable system cannot tolerate.
So be careful when you design with conditional stability. And only use one amplifier stage with infinite DC gain in your feedback path. Two is not better than one in this case.
In looking at conditional stability it is useful to think of what frequency a linear feedback LTI system generates when it becomes just unstable. When this happens it becomes an oscillator at one frequency and one frequency only.
Some designers like to put two amplifiers with infinite DC gain in series in their feedback path, believing that two must be better than one. This is one way to create a conditionally stable system. It is perfectly stable but may also be found in a state of violent self oscillation. Once it has become unstable, it is unable to recover by itself.
What happens is that the oscillating system has a much lower effective open loop gain than normal, due to clipping of the signal in some of the amplifiers. A large reduction of effective gain is just what a conditionally stable system cannot tolerate.
So be careful when you design with conditional stability. And only use one amplifier stage with infinite DC gain in your feedback path. Two is not better than one in this case.
In looking at conditional stability it is useful to think of what frequency a linear feedback LTI system generates when it becomes just unstable. When this happens it becomes an oscillator at one frequency and one frequency only.