BIBO stability

In signal processing, specifically control theory, bounded-input, bounded-output (BIBO) stability is a form of stability for linear 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 a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response be absolutely integrable, i.e., its L¹ norm exists.

For a discrete time LTI system, the condition for BIBO stability is that the impulse response be absolutely summable, i.e., its ${\displaystyle \ell ^{1}}$ norm exists.

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