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The cohomology of the moduli space of controllable linear systems. (English) Zbl 0768.93009
Summary: We explicitly describe, by generators and relations, the cohomology ring of the manifold \(\Sigma_{n,m}({\mathbf F})\) of controllable linear systems having \(m\) inputs and state-space dimension \(n\). It is shown that the cohomology ring of \(\Sigma_{n,m}({\mathbf F})\) is isomorphic to the invariant cohomology ring of a product of projective spaces. Estimates for the cup length of the cohomology ring are obtained.

93B05 Controllability
93B27 Geometric methods
93C05 Linear systems in control theory
14D22 Fine and coarse moduli spaces
14F45 Topological properties in algebraic geometry
15A21 Canonical forms, reductions, classification
Full Text: DOI
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