BIBO Stability

Boundedness

Let $u(t)/u[k]$ be a real-valued signal defined for $t\ge 0/k\in {\mathbb{Z}}_{{\ge }_0}$. Then $u$ is bounded if there exists $\bar{u}\in \mathbb{R}$, $\bar{u}>0$ such that $-\bar{u}<u(t)<\bar{u}$ for all t and k greater than 0.

Both are bounded.

Signals that explode (either by design or unintentionally) are unbounded.

Bounded Input Bounded Output (BIBO)

A LTI system $P(s)/G[z]$ is BIBO stable if every bounded input produces a bounded output.

• Assuming $P(s)/G[z]$ is real, rational, and proper. Then they are stable if and only if it is BIBO stable.

BIBO Stable <> Stable (IF AND ONLY IF)