Why do we care if a system is BIBO stable?

1. Is the system BIBO stable Why or why not?
2. What are the conditions for a BIBO stable system?
3. What is the requirement of BIBO stability in control system?
4. Under what conditions does BIBO stability imply asymptotic stability?

Is the system BIBO stable Why or why not?

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).

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.

What is the requirement of BIBO stability in control system?

Bounded-Input Bounded-Output Stability

(13.12) is said to be BIBO stable if and only if, whichever is the bounded input |u(t)|≤U, t ≥ 0, the output y(t) of the state equation is also bounded. For instance, if holds for the transfer matrix M(s) = C(sI−A)⁻¹B + D, the relevant state equation is BIBO stable.

Under what conditions does BIBO stability imply asymptotic stability?

130-1) 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.