A simplified algorithm for testing stability of discrete systems via bilinear continued fractions

An algorithm for testing stability of discrete systems, using methods in the
z
-domain exclusively, is presented. The algorithm is based on expanding the bilinear discrete reactance function into
z
-domain continued fractions in a mixed fashion. It is faster than Steffen's algorithm and compares favorably with the commonly used tabular form of testing stability. The new algorithm is implemented in a form of a table that is considered the bilinear image, in the z-domain, of the generalized Routh Table of continuous-time systems. Illustrative examples are included.