SciELO - Scientific Electronic Library Online

vol.38 issue3On a new class of generalized difference sequence spaces of fractional order defined by modulus functionA new type of generalized closed set via γ-open set in a fuzzy bitopological space 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.38 no.3 Antofagasta Aug. 2019 


Controllability of affine systems on free Nilpotent Lie groups Gm,ᵣ

1Yildiz Technical University, Department of Mathematics, Davutpasa Campus, 34220, Istanbul, Turkey. e-mail :

2Yildiz Technical University, Department of Mathematics, Davutpasa Campus, 34220, Istanbul, Turkey. e-mail :


Controllability properties of affine control systems on free nilpotent Lie groups are examined and controllability of affine systems on thiskind of Lie groups are characterized by the help of their associated bilinear parts. In order to show this, an automorphism in the algebra level is found, authomosrpism orbit of the system is calculated and its properties are studied.

Keywords: Controllability; Affine algebra; Automorphism; Derivation; Free nilpotent Lie group

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The second author was supported by TUBITAK- The Scientific and Technological Research Council of Turkey.


[1] V. Jurdjevic and G. Sallet, “Controllability properties of affine systems”,SIAM Journal on Control and Optimization, vol. 22, no. 3, pp. 501-508, 1984, doi: 10.1137/0322030. [ Links ]

[2] A. Kara and L. San Martin , “Controllability of affine control systems for the generalized Heisenberg lie groups”, International Journal of Pure and Applied Mathematics, vol. 29, no. 1, 2006. [On line]. Available: ]

[3] V. Jurdjevic, Geometric Control Theory. Cambridge: Cambridge University Press, 1996, doi: 10.1017/CBO9780511530036. [ Links ]

[4] A. Bonfiglioli, F. Uguzzoni and E. Lanconelli, Stratified Lie Groups and Potential Theory for Their Sub-Laplacians, (Springer Monographs in Mathematics), Berlin: Springer, 2008, doi: 10.1007/978-3-540-71897-0. [ Links ]

[5] M. Grayson and R. Grossman, “Models for free nilpotent Lie algebras”, Journal of Algebra, vol. 135, no. 1, pp. 177-191, Nov. 1990, doi: 10.1016/0021-8693(90)90156-I. [ Links ]

[6] H. Sussmann, “Some properties of vector field systems that are not altered by small perturbations”, Journal of Differential Equations, vol. 20, no. 2, pp. 292-315, Mar. 1976, doi: 10.1016/0022-0396(76)90109-1 [ Links ]

Received: April 2018; Accepted: November 2018

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License