The answer is yes whether you use a fixed DC link with PWM or variable DC link with PWM. Earlier AC drives used a DC link chopper as the DC/DC converter to control maximum output voltage and PWM to vary the frequency. Modern drives just use variable voltage variable frequency (VVVF) PWM to do this all at once.
Regardless of which technique one adopts the maximum voltage will always be the input DC link voltage so that any output circuitry will have to be designed to cope with this.
Most commercial PWM are of the VVVF type and where the max voltage will be the input DC link voltage. For three phase 400V it will be sqrt(2)*400 = 565V.
I'm assuming you mean you want to control the amplitude of the AC output voltage of the inverter, and the answer (as noted by Gregory) is yes. The method of control depends on the type of (the design of) the converter but typically involved tracking the voltage against a sinusoidal control and a triangular signal at Fs, the fundamental frequency of the inverter. I'd suggest searching www.allaboutcircuits.com or a book on Power Electronics by Mohan or one of the several other university level texts.
The most common asynchronous motor drive uses a 6 pulse diode bridge input and a PWM IGBT inverter. Hence, the dc link voltage is fixed, at approximately 1.35 x input L-L rms voltage. There may also be qa dc link capacitor for voltage ripple control. And, the motor speed control is V/f = constant, meaning that to obtain 50% motor speed, frequency "f" of the voltage to the motor is half, and voltage "V" to the motor is also half.
You can control both depending on your control target. At the meantime, you need to synchronize your inverter voltage with the utility or load (voltage and frequency).
Yes. You can control output voltage of inverter using two methods.
(i) by changing amplitude of Supply DC link and (ii) by changing duty cycle of control circuit.
In control circuit one can use Sinusoidal Pulse Width Modulation (SPWM) technique.
In which you can compare 50/60 Hz sinewave (call "Reference wave") with 5KHz or more than that triangular wave(called "Carrier Wave". from which you get pulses for Inverter Switches.
In this by changing Amplitude of Reference Wave (keeping constant amplitude of Carrier wave) you can change output of Inverter.
The RMS of the ouput voltage of a PWM inverter can be regulated. However, in a real application, the required control must keep the high quality of the output signal despite of the nature of the load (linear and nonlinear). Then, the control loop objective is the tracking of a reference waveform which is different to only regulate the RMS or the amplitude. In other words, with a nonlinear load connected at the ouput of the inverter you can have the desired RMS with a undesired waveform. As a first approach, you can try using a PID controller in simulations.