The relationships between the classical Bezout matrix and Bernstein Bezout matrix are given by the transformation matrix of the standard power basis and Bernstein polynomial basis. Meanwhile, a generalized linear control system for the Bernstein polynomial basis is established from the classical one, and a kind of generalized controllability/observabilitytype matrices is constructed correspondingly. Finally, connections between Bernstein Bezout matrix and generalized controllability/observabilitytype matrices are discussed. The results obtained are parallel to the previous ones for the standard power basis.