BIBO stability of $y(t)=\int_{-\infty}^{t}{x(\tau)d\tau}$

1. How do you determine BIBO stability?
2. What do you mean by BIBO stability?
3. Is the circuit BIBO stable?
4. Which of the following system is BIBO stable?

How do you determine BIBO stability?

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 do you mean by BIBO stability?

Bounded input, bounded output (BIBO) stability is a form of stability often used for signal processing applications. The requirement for a linear, shift invariant, discrete time system to be BIBO stable is for the output to be bounded for every input to the system that is bounded.

Is the circuit BIBO stable?

Basically, a system is BIBO stable if and only if nice inputs produce nice outputs.

Which of the following system is BIBO stable?

In this signal, as t → ∞ , the impulse response value is not approaching 0 value. Hence it's BIBO stable. A system is bounded input bounded output (BIBO) stable if the output is guaranteed to be bounded for every bounded input. The magnitude of a sum of terms is less than or equal to the sum of their magnitudes.