<abstract xmlns="http://www.w3.org/1999/xhtml"> We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input control systems). A brief comparison of these classification results with existing results concludes the paper. </abstract>

We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input control systems). A brief comparison of these classification results with existing results concludes the paper.

Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)0

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)

We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank...

Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)₀

Published Online: Sep 21, 2017

Page range: 45 - 65

Received: Apr 01, 2015

Accepted: Jun 30, 2015

DOI: https://doi.org/10.1515/auom-2016-0027

Keywords
Left-invariant control system, state space equivalence, pseudo-orthogonal group

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)0

Published Online: Sep 21, 2017

Page range: 45 - 65

Received: Apr 01, 2015

Accepted: Jun 30, 2015

DOI: https://doi.org/10.1515/auom-2016-0027

KeywordsLeft-invariant control system, state space equivalence, pseudo-orthogonal group

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)₀

Keywords
Left-invariant control system, state space equivalence, pseudo-orthogonal group