In this paper, a controllability analysis is treated. The previous controllability ayalysis is focused on the global controllability or local controllability. However there exist systems which have a singular state of the controllability. Previous research often doesn't care about the singularity. This paper gives the definition of a controllability with the singularity, and extends the previous theorems for the new definition. Finally, for example, the controllability of a single rotor spacecraft system is analyzed.
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