It sounds like you are trying to pitch something, and I don't buy it.
Anyhow, the impedance affect the current supplied to the circuits do to the impedance inside the battery. As the battery starts to degrade, impedance rises, and thus provide less voltage because of the voltage drop of the internal resistance. Circuit have something called a regulator that keeps the DC level in the level that the circuits need, if it wasn't stable those ICs would be screwed up, so have some faith the regulator is doing it's job keeping the DC level stable. At a certain voltage level, the regular cannot do it's job, and time for a new battery. Possibly batteries have an IC inside that kills it if it cannot provide enough for the regulator.
You can take or leave what I say. Trying to pitch something? Are you kidding? Start from the ground up with a good power supply, which in the case of a battery, start with the battery and go from there. I don't care if you buy it or not, I am not selling anything. I have built amps and preamps and Woo Audio uses my design for the pseudo dual power supply because it works.