Bernstein Bezout Matrix with Applications to Polynomial Stability

摘要

The Bernstein Bezoutian with respect to the Bernstein polynomials basis is investigated. A general linear control system under the Bernstein polynomials basis is established from the classical one, and a kind of generalized controllability/observability matrices are constructed. Connections between Bernstein Bezoutian and generalized controllability/observability matrices are discussed. Some results for polynomial stability in terms of the Bernstein Bezoutian are obtained, which generalize the corresponding classical Fujiwara-Hermite and Routh-Hurwitz criteria.