Pommaret, J. F.; Quadrat, A. Generalized Bézout identity. (English) Zbl 1073.93516 Appl. Algebra Eng. Commun. Comput. 9, No. 2, 91-116 (1998). Summary: We describe a new approach to the generalized Bézout identity for linear time-varying ordinary differential control systems. We also explain when and how it can be extended to linear partial differential control systems. We show that it only depends on the algebraic nature of the differential module determined by the equations of the system. This formulation shows that the generalized Bézout identity is equivalent to the splitting of an exact differential sequence formed by the control system and its parametrization. This point of view gives a new algebraic and geometric interpretation of the entries of the generalized Bézout identity. Cited in 11 Documents MSC: 93B25 Algebraic methods 13N10 Commutative rings of differential operators and their modules Keywords:Generalized Bézout identity; Controllability; Parametrization; Janet sequence; Formal integrability; D-module; Commutative algebra PDFBibTeX XMLCite \textit{J. F. Pommaret} and \textit{A. Quadrat}, Appl. Algebra Eng. Commun. Comput. 9, No. 2, 91--116 (1998; Zbl 1073.93516) Full Text: DOI