Abstract
A special kind of port-controlled bilinear Hamilton system is researched. The controllability distribution and observability codistribution of the kind of port-controlled bilinear Hamilton systems are disused by using differential geometric of nonlinear control system. Lie brackets between input vector field and control vector field, Lie derivative of output function along input vector field and control vector field are researed. At the same time, the controllability and observability of the port-controlled bilinear Hamilton systems are disused Lie brackets between input vector field and control vector field. Then the relation between the controllability and observability is studied. The equivalence condition of controllability and observability is given.
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