Displaying similar documents to “Non-overlapping control systems on Lie groups.”

On the equivalence of control systems on Lie groups

Rory Biggs, Claudiu C. Remsing (2015)

Communications in Mathematics

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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.

Controllability of invariant control systems at uniform time

Víctor Ayala, José Ayala-Hoffmann, Ivan de Azevedo Tribuzy (2009)

Kybernetika

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Let G be a compact and connected semisimple Lie group and Σ an invariant control systems on G . Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time s Σ such that the system turns out controllable at uniform time s Σ . Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if A = ⋂ t > 0 A ( t , e ) denotes the reachable set from...