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Following from this assumption, the transfer function of the system must have poles on the left-half side of the complex plane i.e. the real parts of the potentially complex roots of the denominator polynomial are negative. I know about the Routh-Hurwitz stability criterion, and have used it on many examples which do pass the criterion, but I still can't find any generality. If it's something that always allows this to happen, it must be something with Kirchhoff's Laws. What do you think?

Good day!