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Title: Null controllability of planar bimodal piecewise linear systems
Authors: Liu, X.
Lin, H. 
Chen, B.M. 
Keywords: continuous-time systems
geometric method
hybrid systems
null controllability
piecewise linear systems
Issue Date: Apr-2011
Citation: Liu, X., Lin, H., Chen, B.M. (2011-04). Null controllability of planar bimodal piecewise linear systems. International Journal of Control 84 (4) : 766-782. ScholarBank@NUS Repository.
Abstract: This article investigates the null controllability of planar bimodal piecewise linear systems, which consist of two second order LTI systems separated by a line crossing through the origin. It is interesting to note that even when both subsystems are controllable in the classical sense, the whole piecewise linear system may be not null controllable. On the other hand, a piecewise linear system could be null controllable even when it has uncontrollable subsystems. First, the evolution directions from any non-origin state are studied from the geometric point of view, and it turns out that the directions usually span an open half space. Then, we derive an explicit and easily verifiable necessary and sufficient condition for a planar bimodal piecewise linear system to be null controllable. Finally, the article concludes with several numerical examples and discussions on the results and future work. © 2011 Taylor & Francis.
Source Title: International Journal of Control
ISSN: 00207179
DOI: 10.1080/00207179.2011.576433
Appears in Collections:Staff Publications

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