Out of curiosity. Are the "external model" and "grow unbounded" parts necessary conditions? Doesn't "linear system" already imply a mathematical model? Doesn't "unstable system" imply at least 1 term tending to infinity? Anyway, I guess the argument against is that poles in the right half of the complex plane have positive real parts. So having at least one pole there will result in an unstable system. By the way, I wondered if the functions need to be continuous and/or holomorphic?
To be a little more clear, all of those were meant as examples of things that are false, and can be proven as false (null hypotheses, of sorts). "External model," is because the system could have internally unstable modes that aren't represented in the external model (canceled by zeroes of the transfer function). So it would be technically correct to say that a system is stable even if one of its poles is located in the positively real half of the plane, under the condition that it also has a zero at the same location (externally stable). The boundedness is extraneous information, that's true. Does need to be continuous, though. A
discrete time, linear system is generally stable if its poles lie anywhere within the unit circle.
Despite what many in the media etc. claim, there has apparently been research (started years ago) into this so I won't argue that. Cedars-Sinai cooperated with a bioscience company : https://www.cedars-sinai.org/newsroom/cedars-sinai-statement-on-uv-a--technology/ . More detailed sources add that they hope to get approval to test this on people in the nearby future.
Well I'll be damned. I'll reserve further judgement until they've passed clinical trials in humans, and it may be worth noting that it's specifically UV-A, but that is very interesting. I was potentially wrong. Thanks for pointing that out.