Stability of a system
For BIBO stability in the case of discrete time, there is a necessary and sufficient condition given by $\sum |h[n]| &lt; \infty$ 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.