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Generalized linear systems: Geometric and structural approaches. (English) Zbl 0679.93048
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.

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
Full Text: DOI
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