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On the equivalence of control systems on Lie groups
Communications in Mathematics, Tome 23 (2015) no. 2, pp. 119-129 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.
We consider state space equivalence and feedback equivalence in the context of (full-rank) left-invariant control systems on Lie groups. We prove that two systems are state space equivalent (resp.~detached feedback equivalent) if and only if there exists a Lie group isomorphism relating their parametrization maps (resp. traces). Local analogues of these results, in terms of Lie algebra isomorphisms, are also found. Three illustrative examples are provided.
Classification : 22E60, 93B27
Keywords: left-invariant control system; state space equivalence; detached feedback equivalence 
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Biggs, Rory; Remsing, Claudiu C. On the equivalence of control systems on Lie groups. Communications in Mathematics, Tome 23 (2015) no. 2, pp. 119-129. http://geodesic.mathdoc.fr/item/COMIM_2015_23_2_a2/

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