### Non-overlapping control systems on Lie groups.

Y. Chae, Y. Lim (1994)

Semigroup forum

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Y. Chae, Y. Lim (1994)

Semigroup forum

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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 $\Sigma $ 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 ${s}_{\Sigma}$ such that the system turns out controllable at uniform time ${s}_{\Sigma}$. 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 $A={\bigcap}_{t>0}A(t,e)$ denotes the reachable set from...

S. Trybuła (1987)

Applicationes Mathematicae

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Fritz Colonius, Roberta Fabbri (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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For systems with slowly varying parameters the controllability behavior is studied and the relation to the control sets for the systems with frozen parameters is clarified.

A. Plis (1973)

Annales Polonici Mathematici

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Stanisław Łojasiewicz, Jr. (1979)

Annales Polonici Mathematici

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Hans-Dieter Burkhard (1988)

Banach Center Publications

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Czesław Olech, Bronisław Jakubczyk, Jerzy Zabczyk (1985)

Banach Center Publications

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J. Lewoc (1971)

Applicationes Mathematicae

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M. Medveď (1977)

Annales Polonici Mathematici

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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.

Hector J. Sussmann (1985)

Banach Center Publications

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