Stability

A linear CT system $T$ is said to be bounded-input bounded-output stable (BIBO) if there is a constant $K\ge 0$ such that $\Vert y{\Vert }_{\infty }\le K\Vert x{\Vert }_{\infty }$ for all bounded inputs $x$ and outputs $y$.

i.e., bounded inputs produce bounded outputs

Stable systems are important in engineering. This often means that we can control how they behave.¹ Unstable systems are also dangerous — and can lead to component damage or failure.

Determining whether a system is BIBO stable or not is done by giving a bounded input and seeing if the result is unbounded.

Footnotes

1. More or less from one of Prof Najm’s many lectures. ↩