A supplement to "The roles of Sylvester and Bezoutian matrices in the historical study of stability of linear discrete-time systems"

In this supplement, we present the stability criterion of Nour-Eldin, based on the Cauchy index and Hankel matrix arguments, and its reduced form, based on reduced Schur-Cohn-Fujiwara criterion. This simplification of the Nour-Eldin criterion is further elaborated by Anderson and Mansour [1991]. A related result, based on reduced Markov stability criterion, was obtained by Mansour and Anderson [1990].