Theorem: BIBO stability Stable

Suppose is real, rational, and proper. Then is stable if and only if is BIBO stable.

We will prove this for strictly proper.

First, we prove Stable BIBO stable.

  • Given: is stable, real, rational and strictly proper.
  • WTS: BIBO stable

Proof:

  • Consider a bounded input signal which implies that such that . [definition of bounded]
  • Let . Then:

Then, we prove BIBO stable.

  • Given: is BIBO stable, real, rational and strictly proper.
  • WTS: BIBO stable

Last time we