BIBO

Info

An LTI system is bounded-input-bounded-output stable if every bounded input produces a bounded output.

We basically want to prove that $\left|x\left(t\right)\right|\le \bar{u}\le \infty$

Theorem

Assume $P\left(s\right)$/$G\left[z\right]$ is real, rational and proper (defined in Transfer Functions). Then $P\left(s\right)$/$G\left[z\right]$ is stable if and only if it is BIBO stable.

Our shortcut here, is that we check for normal stability and then assume it is BIBO stable by the above theorem.