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The topology of a moduli space for linear dynamical systems. (English) Zbl 0613.93008
The author studies the quotient space obtained by acting on the set of all linear systems without outputs, of a fixed dimension and number of controls, by change of basis in the state-space. In particular, he establishes that the mod 2 Betti numbers of these spaces coincide with those of certain Grassmannians. Some results had been obtained earlier for systems over the complex numbers; here the treatment applies over the reals. The paper is very well-written and provides an excellent introduction to the area.
Reviewer: E.Sontag

MSC:
93B10 Canonical structure
54H20 Topological dynamics (MSC2010)
93C05 Linear systems in control theory
14J10 Families, moduli, classification: algebraic theory
93B05 Controllability
93B20 Minimal systems representations
93B25 Algebraic methods
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