Displaying similar documents to “On the number of control sets on compact homogeneous spaces.”

Controllability of invariant control systems at uniform time

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



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...

Controllability for systems with slowly varying parameters

Fritz Colonius, Roberta Fabbri (2003)

ESAIM: Control, Optimisation and Calculus of Variations


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.


Czesław Olech, Bronisław Jakubczyk, Jerzy Zabczyk (1985)

Banach Center Publications


On the equivalence of control systems on Lie groups

Rory Biggs, Claudiu C. Remsing (2015)

Communications in Mathematics


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.