Q:

Stability of a system

Is the system $y[n] = x[n] - x[n-1]$ stable or unstable ? 
If unstable, can you please give some examples of input signals for which the system becomes unstable? 

A:

For BIBO stability in the case of discrete time, there is a necessary and sufficient condition given by $\sum |h[n]| < \infty$ that is if the impulse response is absolute summable then the system is BIBO stable. Clearly
$$h[n] = \delta[n] - \delta[n-1]$$ and it has a finite support, the impulse response is absolutely summable and therefore BIBO stable.

