Schur-Stability Test

[-InnoXenT-]

I have done some problems and observe that for Schur Array Stability Test of characteristic equation with order N, I have to do the stability check (compare the first number and last number) for (N-1) times, and I'd like to know whether each comparison means anything. From my observation, for a causal-system, if absolute value of first number is greater than absolute value of last number, I think that means one pole lies inside the unit circle. To make it more understand about my question,

Suppose I have "a" as the first number of an array, and "b" as the last number of an array (and supposed the system is causal system)

$\left| a\,\right|$ _ $\left| b\,\right|$

If $\left| a\,\right| > \left| b\,\right|$ means we have one more pole lies inside the unit circle
$\left| a\,\right| = \left| b\,\right|$ means we have one more pole lies on the unit circle
$\left| a\,\right| < \left| b\,\right|$ means we have one more pole lies outside the unit circle,

However, I did not sure if my observation is true or not, because I did some search on google and found nothing. If this is true, therefore we can conclude the number of poles that lie inside/outside/on the unit circle. Thank you krub.