[throwaway87423]

Classical control often restricts itself to Linear systems, and non-linear control is next to useless for non drift-free systems (if you can compute the Lie algebra in the first place). SOS relaxations won't scale, and all bets are off when dealing with contacts.

[tnecniv]

So what's your suggestion when dealing with any non-trivial system? All those issues you mention are true but also active research areas.