About the solutions of linear control systems on Lie groups
DOI:
https://doi.org/10.4067/S0716-09172016000400010Keywords:
Linear control systems, Lie groups, solutions, sistemas de control lineal, grupos de Lie, solucionesAbstract
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.References
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[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).
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[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).
[9] Jouan, Ph., Equivalence of control systems with linear systems on Lie groups and homogeneous spaces, ESAIM: Control Optimization and Calculus of Variations, Vol 16, pp. 956-973, (2010).
Published
2017-03-23
How to Cite
[1]
V. Ayala, A. Da Silva, and E. Kizil, “About the solutions of linear control systems on Lie groups”, Proyecciones (Antofagasta, On line), vol. 35, no. 4, pp. 491-503, Mar. 2017.
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