Malabre, Michel Generalized linear systems: Geometric and structural approaches. (English) Zbl 0679.93048 Linear Algebra Appl. 122-124, 591-621 (1989). Summary: This paper presents a new way of introducing invariant subspaces for generalized systems. This comes from somewhat known geometric algorithms but, in most cases, with initial conditions different from those usually seen in this context. These definitions are shown to be consistent with other ones directly deduced from “classical” approaches like matrix pencil tools or discrete algebraic formalism. The key starting point for their introduction is the extension of structural descriptions for these generalized systems such as have been available for proper systems. Many results from the proper case can thus be extended, for instance the geometric definition for controllability indices and something similar to the famous Morse canonical decomposition of the strictly proper case. Some links with the inversion algorithm are also sketched. Cited in 27 Documents MSC: 93C05 Linear systems in control theory 93B10 Canonical structure 93B27 Geometric methods 93C15 Control/observation systems governed by ordinary differential equations 34A99 General theory for ordinary differential equations Keywords:invariant subspaces; generalized systems; matrix pencil tools; discrete algebraic formalism; definition for controllability indices; Morse canonical decomposition; time-invariant PDF BibTeX XML Full Text: DOI References:  Gantmacher, G., The theory of matrices, (1959), Chelsea, New York  Basile, G.; Marro, G., Controlled and conditioned invariant subspaces in linear system theory, J. optim. theory appl., 3, 306-315, (1969) · Zbl 0172.12501  Rosenbrock, H.H., State space and multivariable theory, (1970), Nelson Wiley London · Zbl 0246.93010  Morse, A.S., Structural invariants of linear multivariable systems, SIAM J. control optim., 11, 3, 446-465, (1973) · Zbl 0259.93011  Thorp, J.S., The singular pencil of a linear dynamical system, Internat. 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