A new formula for the discrete-time system stability test

It is known that while the stability criteria for discrete data systems such as the Schur-Cohn, the Jury, and the Inner tests are complicated in form, the bilinear transformation with the Routh array test is involved in calculation. This note develops a matrix for the binomial product expansion and establishes an inner product formula for evaluating the coefficients of the w polynomial. The new approach enables the use of Routh criterion stability study in discrete time systems as simple and easy as in the continuous case.