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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

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

http://dx.doi.org/10.4067/S0716-09172016000400010 

About the solutions of linear control systems on Lie groups

 

Victor Ayala*

Universidad de Tarapaca

Chile

Adriano Da Silva

Universidade Estadual de Campinas

EyUp Kizil

Universidade de Sao Paulo

Brasil


ABSTRACT

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.


REFERENCES

[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).         [ Links ]

[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).         [ Links ]

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

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

[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.         [ Links ])

[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).         [ Links ]

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

[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).         [ Links ] 7

Victor Ayala

Instituto de Alta Investigación,

Universidad de Tarapaca Casilla 7D,

Arica,

Chile

e-mail : vayala@ucn.cl

Adriano Da Silva

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

13.081-970 Campinas-SP,

Brasil e-mail :

and

Eyüp Kizil

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

Cx. Postal 668,

CEP: 13.560-970,

Sao Carlos-SP,

Brasil

e-mail : kizil@icmc.usp.br

 

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.

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