I've said this elsewhere in the thread, but stabilizing a dynamically unstable system is half of the reason why control theory remains an active research area instead of a mathematical backwater; this kind of set up is extremely common for aerospace systems. Software is hard to get right - which is why aerospace software has traditionally faced much higher bars for verification than 'traditional' software (and is much more expensive as a result!) The same is true of hardware, which I think many HN commentators forget; the cost of a bolt or connector that is aerospace-grade is typically many times that of a conventional or automotive-grade part, due mostly to extensive testing+verification required for safety.
Most of the scenarios you're describing are dealt with in a few ways:
1. Building systems with sufficient margin to account for this kind of uncertainty; even with passively stable aircraft, these margins exist. Feedback control typically increases these margins.
2. Extensive verification under a wide range of input conditions; this is more challenging (how can you enumerate every possible failure condition?), but usually boils down to some kind of Monte-Carlo sampling or worst-case analysis when those cases can be identified. Here's [0] a neat paper that does this in a more sample-efficient way.
Most of the scenarios you're describing are dealt with in a few ways:
1. Building systems with sufficient margin to account for this kind of uncertainty; even with passively stable aircraft, these margins exist. Feedback control typically increases these margins.
2. Extensive verification under a wide range of input conditions; this is more challenging (how can you enumerate every possible failure condition?), but usually boils down to some kind of Monte-Carlo sampling or worst-case analysis when those cases can be identified. Here's [0] a neat paper that does this in a more sample-efficient way.
[0] https://arxiv.org/abs/1709.06645