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2008 Accessibility of a Class of Generalized Double-Bracket Flows
G. Dirr, U. Helmke
Commun. Inf. Syst. 8(2): 127-146 (2008).


We investigate a generalization of Brockett’s celebrated double bracket flow that is closely related to matrix Riccati differential equations. Using known results on the classification of transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility of the generalized double bracket flow on Grassmann manifolds are derived. This leads to sufficient Lie–algebraic conditions for controllability of the generalized double bracket flow. Accessibility on the Lagrangian Grassmann manifold is studied as well, with applications to matrix Riccati differential equations from optimal control.


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G. Dirr. U. Helmke. "Accessibility of a Class of Generalized Double-Bracket Flows." Commun. Inf. Syst. 8 (2) 127 - 146, 2008.


Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1234.37054
MathSciNet: MR2495870

Keywords: Double bracket flows , Grassmann manifolds , matrix Riccati equations , transitive Lie group actions

Rights: Copyright © 2008 International Press of Boston


Vol.8 • No. 2 • 2008
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