Properties of Hermite's matrices in stability theory
John Maroulas, Stephen Mark Barnett · International Journal of Control · 1979
Hermite's stability criterion is expressed in a simpler form involving a suitably defined observability matrix, and the Hermite matrix H is represented in controllability-observability matrix form. These results are generalized to the ease when the polynomial is expressed in terms of an arbitrary orthogonal basis. The relationship between the Hermitian matrix H and an alternative real symmetric matrix is given, together with the appropriate criteria for root location with respect to the imaginary axis. Also discussed are the form of the inverse of H and applications to Sylvester-form matrices, the reduced Hermite and Schur-Cohn matrices, and the Markov criterion.