An LTI circuit such as one composed of resistors, capacitors, and inductors, in general is a stable LTI system, i.e. its impulse response is one that decays over time. I have no problem with that, as it speaks for itself through laws of energy conservation, but I want to see this from a mathematical standpoint. 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!