Controllability of two-dimensional bilinear systems : restricted controls and discrete-time
DOI:
https://doi.org/10.22199/S07160917.1999.0002.00008Keywords:
Bilinear control systems, Controllability, Two-dimensional systemsAbstract
Given a bilinear control system x = (X+ uY) x with restricted control range, necessary and sufficient conditions for controllability are given under the assumption that the group of the system is Sl (2). These conditions extend known conditions for systems with unrestricted controls and work also for the discrete-time version of the system.
References
[1] C. J. Braga Barros, J. Ribeiro Gonçalves, O. do Rocio and L. A. B. San Martin: Controllability of two-dimensional bilinear systems. Rev. Proyecciones, 15, pp. 111- 139, (1996).
[2] F. Colonius and W. Kliemann : Dynamics and Control. Bírkhiiuser, (1999).
[3] Joó, l. and N. M. Tuan : On controllability of bilinear systems II (controllability in two dimensions). Ann. Univ. Sci. Budapest, 35, pp. 217- 265, (1992).
[4] Jurdjevic, J. : Geometric Control Theory. Cambridge Univ. Press, (1997).
[5] Mittenhuber, D. : The Classification of Global Lie Wedges in Sl (2). Manuscripta Math., 88, pp. 479- 495, (1995).
[6] Sachkov, Y. L. : Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces. Technical report 18/99/M, ISAS Trieste (1999).
[7] San Martin, L. A. B. : lnvariant control sets on flag manifolds. Math. Control, Signals, and Systems, 6, pp. 41-61, (1993).
[8] San Martin, L. A. B. : On global controllability of discrete-time control systems. Math. Control, Signals, and Systems, 8, pp. 279-297, (1995).
[9] San Martin, L. A. B. and P. A. Tonelli : Semigroup actions on homogeneous spaces. Semigroup Forum, 50, pp. 59- 88, (1995).
[2] F. Colonius and W. Kliemann : Dynamics and Control. Bírkhiiuser, (1999).
[3] Joó, l. and N. M. Tuan : On controllability of bilinear systems II (controllability in two dimensions). Ann. Univ. Sci. Budapest, 35, pp. 217- 265, (1992).
[4] Jurdjevic, J. : Geometric Control Theory. Cambridge Univ. Press, (1997).
[5] Mittenhuber, D. : The Classification of Global Lie Wedges in Sl (2). Manuscripta Math., 88, pp. 479- 495, (1995).
[6] Sachkov, Y. L. : Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces. Technical report 18/99/M, ISAS Trieste (1999).
[7] San Martin, L. A. B. : lnvariant control sets on flag manifolds. Math. Control, Signals, and Systems, 6, pp. 41-61, (1993).
[8] San Martin, L. A. B. : On global controllability of discrete-time control systems. Math. Control, Signals, and Systems, 8, pp. 279-297, (1995).
[9] San Martin, L. A. B. and P. A. Tonelli : Semigroup actions on homogeneous spaces. Semigroup Forum, 50, pp. 59- 88, (1995).
Published
2018-04-04
How to Cite
[1]
V. Ayala Bravo and L. A. B. San Martín, “Controllability of two-dimensional bilinear systems : restricted controls and discrete-time”, Proyecciones (Antofagasta, On line), vol. 18, no. 2, pp. 207-223, Apr. 2018.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
