On the equivalence of control systems on Lie groups

Rory Biggs; Claudiu C. Remsing

Communications in Mathematics (2015)

  • Volume: 23, Issue: 2, page 119-129
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Biggs, Rory, and Remsing, Claudiu C.. "On the equivalence of control systems on Lie groups." Communications in Mathematics 23.2 (2015): 119-129. <http://eudml.org/doc/276176>.

@article{Biggs2015,
abstract = {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.},
author = {Biggs, Rory, Remsing, Claudiu C.},
journal = {Communications in Mathematics},
keywords = {left-invariant control system; state space equivalence; detached feedback equivalence; left-invariant control system; state space equivalence; detached feedback equivalence},
language = {eng},
number = {2},
pages = {119-129},
publisher = {University of Ostrava},
title = {On the equivalence of control systems on Lie groups},
url = {http://eudml.org/doc/276176},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Biggs, Rory
AU - Remsing, Claudiu C.
TI - On the equivalence of control systems on Lie groups
JO - Communications in Mathematics
PY - 2015
PB - University of Ostrava
VL - 23
IS - 2
SP - 119
EP - 129
AB - 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.
LA - eng
KW - left-invariant control system; state space equivalence; detached feedback equivalence; left-invariant control system; state space equivalence; detached feedback equivalence
UR - http://eudml.org/doc/276176
ER -

References

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