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Accessibility of the matrix Riccati differential equation
Author(s) -
Dirr G.,
Helmke U.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700722
Subject(s) - riccati equation , algebraic riccati equation , mathematics , differential equation , bracket , matrix (chemical analysis) , pure mathematics , differential (mechanical device) , transitive relation , matrix difference equation , mathematical analysis , algebra over a field , combinatorics , physics , composite material , thermodynamics , mechanical engineering , materials science , engineering
A known result on the classification of transitive Lie group actions on complex Grassmann manifolds is exploited to derive a necessary and sufficient accessibility criterion for the complex matrix differential Riccati equation. We treat both cases, the symmetric as well as the non‐symmetric Riccati equation. Corresponding accessibility results for the real Riccati equation are also available, but not stated here. An application to the accessibility of generalized double bracket flows is given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)