GRASSMANN INVARIANTS, MATRIX PENCILS, AND LINEAR-SYSTEM PROPERTIES

The paper deals with the establishment of relationships between two di fferent types of invariants defined on matrix pencils and polynomial m atrices and highlights their significance in the context of linear sys tems. For general singular matrix pencil sF - G the Grassmann invarian ts of the pencil are introduced as the column, row Grassmann represent atives g(c)(F,G),g(r)(F,G)(t), and their corresponding Plucker matrice s, P-c(F,G),P-r(F,G). The properties of these new invariants of matrix pencils are established. These results provide alternative means for classifying the different families of matrix pencils, which are import ant for the characterization of properties in linear systems. Finally, the relationship between the Grassmann-Plucker invariants of a genera l rational transfer function matrix and the system matrix pencil of a minimal realization is derived. The latter results provide means for t he computation of transfer function Plucker matrices from state space descriptions, as well as enable the linking of state space Kronecker i nvariants to the Plucker invariants of transfer functions.