Alternative to BIBO stability of a system

1. Can an unstable system be BIBO stable?
2. Which system is stable only if it is BIBO stable and asymptotic stable?
3. What is the necessary condition for BIBO stability?
4. Does marginal stability imply BIBO stability?

Can an unstable system be BIBO stable?

A system is BIBO stable if and only if the impulse response goes to zero with time. If a system is AS then it is also BIBO stable (as the poles of the transfer function are a subset of the poles of the system). However BIBO stability does not generally imply internal stability.

Which system is stable only if it is BIBO stable and asymptotic stable?

BIBO stability: A linear system is said to be BIBO stable if the output is bounded for an arbitrary bounded input. Asymptotic stability: It is the same as BIBO stability, except pole-zero cancellation should not be there. If a system is asymptotic stable, then the system is BIBO stable but not vice versa.

What is the necessary condition for BIBO stability?

A system is BIBO stable if every bounded input signal results in a bounded output signal, where boundedness is the property that the absolute value of a signal does not exceed some finite constant.

Does marginal stability imply BIBO stability?

Does marginal stability imply BIBO stability? it is neither stable nor marginally stable.