Abstract
We consider the problem of accessibility and controllability of certain bilinear systems. These evolve on Lie groups whose Lie algebras are the normal real forms of complex simple Lie algebras. Previous results by other authors were obtained under the assumption that the controlled vector field is strongly regular. Our paper is aimed at weakening this requirement, and involves relating the root structure of elements in a Lie algebra as above to the nodal connection graphs obtained from their standard matrix representations. This is in turn related to a standard irreducibility assumption on the uncontrolled vector field. The abstract results on generation of Lie algebras are of some independent interest.
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The work of this author was supported in part by a Fulbright grant, while she was visiting the Arizona State University, and by the Centro de Matemática da Universidade de Coimbra/INIC.
The work of this author was partially supported by AFOSR Contract No. 85-0224A.
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Silva, F., Crouch, P.E. Controllability on classical Lie groups. Math. Control Signal Systems 1, 31–42 (1988). https://doi.org/10.1007/BF02551234
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DOI: https://doi.org/10.1007/BF02551234