Helmke, Uwe The topology of a moduli space for linear dynamical systems. (English) Zbl 0613.93008 Comment. Math. Helv. 60, 630-655 (1985). 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 Cited in 13 Documents 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 Keywords:moduli spaces of linear control systems PDFBibTeX XMLCite \textit{U. Helmke}, Comment. Math. Helv. 60, 630--655 (1985; Zbl 0613.93008) Full Text: DOI EuDML