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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.

MSC:
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
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