Notes on the stability criterion for linear discrete systems

It is known that linear time-invariant discrete systems can be described by constant coefficient linear difference equations. One of the problems in the analysis of such systems is the test for stability. These tests involve both graphical procedures such as Nyquist locus, Bode diagrams and the root-locus, and analytical methods such as Schur-Cohn
¹
or Routh-Hurwitz criteria. Because of the high-order determinants to be evaluated using the present form of the Schur-Cohn criterion, many authors have used the bilinear transformation which maps the inside of the unit circle in the z = e
^Ts
plane into the left half of the w plane and then applied the Routh-Hurwitz criterion. This transformation involves algebraic manipulation which for higher-order systems becomes complicated.