Contents In this paper, first the apportioning of null-space-vector duty ra
tio between two null-space-vectors for the conventional three-phase voltage
source sinusoidal pulse width modulation inverter is derived. To achieve c
lean sinusoidal input current, adjustable power factor and bidirectional po
wer flow and step-up/down output DC voltage, analytic duty cycle control la
ws based on the derived null-space-vector duty ratio are then derived. As a
result, the popularly used state-space technique can be extended easily fo
r modeling a process that allows to obtain any kind of the desired transfer
functions and dynamic responses. Based on these dynamic responses obtained
the regulators of closed loop control system can be designed or adjusted p
roperly. Finally, some simulated and measured results are presented for dem
onstration.