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The relationships between the methods of Hermite, Schur and Lyapunov in the stability theory of polynomials. (Russian, English) Zbl 1102.26301
Zh. Vychisl. Mat. Mat. Fiz. 42, No. 9, 1283-1289 (2002); translation in Comput. Math. Math. Phys. 42, No. 9, 1235-1241 (2002).
The classical method of the symmetrical and Hermite forms in a separation theory of the radicals of polynomials is based on an application of an inertia law of quadratic forms. The connection between methods of Hermite, Schur and Lyapunov in stability theory of polynomials with usage of a special representation of the Bezu’s matrix is established. A generalization of the obtained results on operational beams is shown.
MSC:
26C10 Real polynomials: location of zeros
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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