SciELO - Scientific Electronic Library Online

vol.35 issue4Some geometric properties of lacunary Zweier Sequence Spaces of order aAn equivalence in generalized almost-Jordan algebras author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.4 Antofagasta Dec. 2016 

About the solutions of linear control systems on Lie groups


Victor Ayala*

Universidad de Tarapaca


Adriano Da Silva

Universidade Estadual de Campinas

EyUp Kizil

Universidade de Sao Paulo



In this paper we prove in details the completeness of the solutions of a linear control system on a connected Lie group. On the other hand, we summarize some results showing how to compute the solutions. Some examples are given.

Keywords : Linear control systems, Lie groups, solutions.

AMS 2010 subject classification : 16W25; 93B05; 93C05.


[1]    Ayala, V. and Tirao, J. Linear control systems on Lie groups and con-trollability, Eds. G. Ferreyra et al., Amer. Math. Soc., Providence, RI, (1999).

[2]    Ayala, V. and San Martin, L., Controllability properties of a class of control systems on Lie groups. Lectures Notes in Control and Information Science, (2001).

[3]    Ayala, V. and Da Silva, A., Controllability of linear systems on Lie groups with finite semisimple center. Submitted to SIAM Journal, (2016).

[4]    Ayala, V, and Silva, A., Control sets of linear systems on Lie groups. Submitted to Nonlinear Differential Equations and Applications, (2016).

[5]    Ayala, V, Kizil, E. and Tribuzy, I., On an algoritm for finding derivations of Lie algebras. Proyecciones Mathematical Journal, Vol 31, No. 1, pp. 81-90, (2012. )

[6]    Da Silva, A., Controllability of linear systems on solvable Lie groups, SIAM Journal on Control and Optimization, Vol 54, No. 1, pp. 372-390, (2016).

[7]    Jouan, Ph., Controllability of linear Systems on Lie group, Journal of Dynamics and Control Systems, Vol 17, pp. 591-616, (2011).

[8]    Jouan, Ph. and Dath M., Controllability of linear systems on low dimensional nilpotent and solvable Lie groups, Journal of Dynamics and Control Systems, Vol 22, pp. 207-225, (2016). 7

Victor Ayala

Instituto de Alta Investigación,

Universidad de Tarapaca Casilla 7D,



e-mail :

Adriano Da Silva

Instituto de Matemática Universidade Estadual de Campinas Cx. Postal 6065,

13.081-970 Campinas-SP,

Brasil e-mail :


Eyüp Kizil

Instituto de Ciencias Matematicas e de Computacao, Universidade de São Paulo,

Cx. Postal 668,

CEP: 13.560-970,

Sao Carlos-SP,


e-mail :


Received : July 2016. Accepted : September 2016


*Supported by Proyecto Fondecyt No. 1150292, Conicyt.

Supported by Fapesp Grant No. 2016/11135-2.

Supported by Tubitak Grant No. 116C081.

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License