✦ LIBER ✦

Controllability of bilinear systems

✍ Scribed by U. Piechottka; P.M. Frank

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 264 KB
Volume: 28
Category: Article
ISSN: 0005-1098
DOI: 10.1016/0005-1098(92)90160-h

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✦ Synopsis

The goal of this paper is to find conditions for the controllability of homogeneous-in-the-state bilinear systems in state spaces of dimensions two and three. The cases where the system matrices of such systems generate a Lie algebra equal to the dimension of the state space are considered, i.e. where the corresponding strictly bilinear system is controllable. For the two-dimensional case it turns out that there are only two situations when the strictly bilinear system is controllable but the homogeneous-in-the-state bilinear system is not. By checking the vector fields on the boundaries of the reachable sets obtained in these two situations, one can easily determine whether the homogeneous-in-the-state bilinear system is controllable or not, provided the Lie algebra of the system matrices has rank two. This approach is extended to the three-dimensional case and thus previously obtained results can be generalized.

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