#### Identifier

etd-0711102-152933

#### Degree

Doctor of Philosophy (PhD)

#### Department

Mathematics

#### Document Type

Dissertation

#### Abstract

In this work we study controllability properties of linear control systems on Lie groups as introduced by Ayala and Tirao in [AT99]. A linear control system _x0006_Σ Lie group G is defined by x' = X(x) + Σ^{k}_{j=1} u_{j}Y_{j}(x), where the drift vector field X is an infinitesimal automorphism, u_{j} are piecewise constant functions, and the control vectors Y_{j} are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by _x0006_Σ are presented in Chapter 3. Under a condition similar to the Kalman condition which is needed for controllability of linear control systems on R^{n}, Ayala and Tirao showed local controllability of the system Σ _x0006_at the group identity e. An alternate proof of this result is obtained using the Lie theory of semigroups. More importantly, an extension of this result is proved. These results are contained in Chapter 4. Finally, in Chapter 5 an example on the Heisenberg Lie group is presented and its properties are proved using the theory developed.

#### Date

2002

#### Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

#### Recommended Citation

Cardetti, Fabiana, "On properties of linear control systems on Lie groups" (2002). *LSU Doctoral Dissertations*. 1074.

http://digitalcommons.lsu.edu/gradschool_dissertations/1074

#### Committee Chair

Guillermo Ferreyra