BIBO stability

In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for signals and systems that take inputs. If a system is BIBO stable, then the output will be bounded for every input to the system that is bounded.

A signal is bounded if there is a finite value ${\displaystyle B>0}$ such that the signal magnitude never exceeds ${\displaystyle B}$, that is

For discrete-time signals: ${\displaystyle \exists B\forall n(\ |y[n]|\leq B)\quad n\in \mathbb {Z} }$

For continuous-time signals: ${\displaystyle \exists B\forall t(\ |y(t)|\leq B)\quad t\in \mathbb {R} }$