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It all depend on your desinge of the inverter and the type of oscilator used,some of the ic's used as oscilators has an in buid pwm control by feeding in feed back loop to the pwm control pin,eg SG3524.3525.3526.TL494 and so on.then the need of controling H-BRIDGE as you mention has nothing to do with the output voltage,the voltage control usualy come from the oscilator.