E. I. Jury gives a brief historical review of the work of four well known mathematicians in the nineteenth century which affected research on stability and related topics until now. These mathematicians are C. Hermite, E. J. Routh, A. M. Lyapunov and A. Hurwitz.
Based on the work of Sylvester the connection between the resultant determinants and Hurwitz matrix minors is established. Orlando’s formulae are presented, connections with Hermite matrix are shown. Then reduced Hermite criterion and reduced Hurwitz criterion are presented and connections with Routh stability table and Lyapunov’s second method are discussed. A connection between the Bezoutian and the Hermite matrix is obtained. Five important applications of the Hurwitz criterion are brought into light. Some comments regarding the Lienard-Chipart criterion and the best possible simplification of the Hurwitz criterion for stability are made. Then some conclusions and an interesting list of references covering 100 years are given.
Of course, all results are given without proofs. The paper may be of interest for mathematicians working in algebra, numerical mathematics or history of mathematics.
For the entire collection see [Zbl 0846.00042].