EXTERIOR ALGEBRA AND INVARIANT SPACES OF IMPLICIT SYSTEMS - THE GRASSMANN REPRESENTATIVE APPROACH

The matrix pencil algebraic characterisation of the families of invari ant subspaces of an implicit system S(F, G) : Fz = Gz F, G is-an-eleme nt-of R(m x n), is further developed by using tools from Exterior Alge bra and in particular the Grassmann Representative g(nu) of the subspa ce nu of the domain of (F, G). Two different approaches are considered : The first is based on the compound of the pencil C(d)(sF - G), which is a polynomial matrix and the second on the compound pencil sC(d)(F) - C(d)(G), d = dim nu. For the family of proper spaces of the domain of (F, G), m greater-than-or-equal-to d, new characterisations of the invariant spaces nu are given in terms of the properties of g(nu) as g eneralised eigenvectors, or invariance conditions for the spaces LAMBD A(p)nu, p = 1, 2, ..., d.