Type of Document	Dissertation
Author	Cardetti, Fabiana
Author's Email Address	fcardet@lsu.edu
URN	etd-0711102-152933
Title	On Properties of Linear Control Systems on Lie Groups
Degree	Doctor of Philosophy (Ph.D.)
Department	Mathematics
Advisory Committee	Advisor Name Title Guillermo Ferreyra Committee Chair Gestur Olafsson Committee Member Jimmie Lawson Committee Member Robert Perlis Committee Member William Adkins Committee Member Young Hak Chun Dean's Representative
Keywords	geometric control theory
Date of Defense	2002-07-10
Availability	unrestricted
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 Σ Lie group G is defined by x' = X(x) + Σkj=1 ujYj(x), where the drift vector field X is an infinitesimal automorphism, uj are piecewise constant functions, and the control vectors Yj are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by Σ are presented in Chapter 3. Under a condition similar to the Kalman condition which is needed for controllability of linear control systems on Rn, Ayala and Tirao showed local controllability of the system Σ 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.
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