Exponential stability conjecture for BIBO stability of hBCS

Let an hBCS be a one-dimensional hyperbolic boundary control system satisfying Assumption

$$. **Exponential stability conjecture.** Any exponentially stable hBCS satisfying Assumption$$

is BIBO stable. The authors state that they have not encountered an exponentially stable hBCS that is not BIBO stable, but no proof or resolution is supplied, so the conjecture remains open.