Stability of passive LTI system Is a passive LTI system will always be a stable(bibo and lyapunov) system?
Or in other words
Passivity of a LTI system implies stability?
If above statements are true then there must be some mathematical relation (description) should be there between passivity and stability, so anyone can help me about its mathematical description (if it exists)
And if passivity doesn't implies stability then there must be some counter example to it to prove my assumption wrong.
So whether my assumption is wrong or there exists a mathematical relation between passivity and stability?
I asked this question here
https://electronics.stackexchange.com/questions/513052/stability-of-passive-networks
but I didn't find any useful answer so I posted it here
A counter-example would be an ideal LC-circuit, which is passive but not BIBO stable: if excited at its resonance frequency, the output grows without bounds. Such systems are sometimes called marginally stable, because they have poles on the stability boundary (the imaginary axis).
Note that if a system is not lossless, i.e., if there is a positive resistance such as in an RLC-circuit, the system is strictly passive, and as a consequence it is also BIBO-stable. I.e., strict passivity implies BIBO-stability (all transfer function poles are in the left half-plane).