Howtosignalprocessing
- What does it mean for a system to be BIBO stable?
- What are the conditions for a BIBO stable system?
- Can a system be BIBO stable but not asymptotically stable?
- Which system is stable only if it is BIBO stable and asymptomatic stable?
What does it mean for a system to be BIBO stable?
A system is said to be input-output stable, or BIBO stable, if the poles of the transfer function (which is an input-output representation of the system dynamics) are in the open left half of the complex plane. A system is BIBO stable if and only if the impulse response goes to zero with time.
What are the conditions for a BIBO stable system?
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.
Can a system be BIBO stable but not asymptotically stable?
A system is asymptotically stable iff all s of A have negative real parts. Since every pole of G(s) is an eigenvalue of A, asymptotic stability (zero-input response) implies BIBO stability (zero-state response). BIBO stability does not in general imply asymptotic stability.
Which system is stable only if it is BIBO stable and asymptomatic 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.
