Abstract
The purpose of these lectures is to present a brief introduction of the role of Grassmannian manifolds in linear control theory. The Riccati equations of linear quadratic optimal control occur naturally as vector fields on the Lagrangian Grassmannian manifolds and exhibit some interesting topological behavior that is discussed in this paper. The feedback structure of linear systems can be deduced through a vector bundle structure on ℙl (ℂ) induced from the “natural bundle” structure on the Grassmannian manifold.
Supported in part by NASA Grant #2384.
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© 1980 D. Reidel Publishing Company
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Martin, C. (1980). Grassmannian Manifolds, Riccati Equations and Feedback Invariants of Linear Systems. In: Byrnes, C.I., Martin, C.F. (eds) Geometrical Methods for the Theory of Linear Systems. Nato Advanced Study Institutes Series, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9082-1_4
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DOI: https://doi.org/10.1007/978-94-009-9082-1_4
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