Causality, Region of Convergence and which side is the system on
If you combine the two requirements (stability => the unit circle must be inside the ROC), and causality (the ROC is given by $|z|&gt;r$ with some real-valued radius $r$), then it follows that $r&lt;1$ must be satisfied. This means that the ROC is outside a circle with radius $r&lt;1$, and, consequently, all poles must be inside this circle with radius $r&lt;1$. So all poles are inside the unit circle (because, by definition, there are no poles in the ROC).