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

In this paper, a historical review of the stability criteria of linear discrete-time systems is presented. In this review the early pioneering works of Hermite, Schur, Cohn, and Fujiwara, and how these paved the way for modern development of other criteria are indicated. It is also mentioned that Sylvester and Bezoutian matrices are the key methods in such developments. Besides this review of early work, some new results and simplifications are brought to light. The paper ends with some important applications of the various stability criteria in diverse fields