# The controllability test for behaviors revisited

Polderman, Jan Willem
(2005)
*The controllability test for behaviors revisited.*
In: 16th IFAC World Congress, July 3-8, 2005, Prague, Czech Republic (pp. pp. 1204-1208).

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Abstract: | Let B = . It is well-know that B is controllable if and only if R(λ) has the same rank for all complex λ. We want to
re-examen the proof of this fundamental result. Denote by B1 the behavior B intersected with set of smooth functions. For B1 the proof is easy and one would expect that the fact that B1 is dense in B would provide a quick and easy proof for the controllability test for B. This, unfortunately, is not true. For the smooth case the proof uses a differential transformation of the behavior. This transformation corresponds to a right unimodular transformation V(E) of R(E) yielding its Smith form. Generally, such a transformation cannot be extended to B since B contains non-smooth trajectories. In this contribution we argue that, despite this fact, the unimodular matrix V(E) defines an injection from B into the behavior defined by the Smith form. With this observation, that is interesting in its own right, the controllability test can be proved relatively easy. |

Item Type: | Conference or Workshop Item |

Copyright: | © 2005 Elsevier |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/68681 |

Official URL: | http://www.elsevier.com/wps/find/bookdescription.cws_home/710500/description |

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