Proof for stability of rational discrete systems

Similar to proof for stability of rational continuous systems, the absolute sum must be convergent.

The absolute sum is

(Assuming two poles (<1) and (>1) of the order >1)

Increasing the number of poles would not make any difference to the proof . are polynomials in n.

Now we know that are absolutely summable.

Finite number of such terms is absolutely summable and hence the Impulse response is absolutely summable.

Therefore ,the system is stable.

The absolute summability of one sided terms of (where p(n) is a polynomial) depends only on and not on the polynomial.