AC Mosfet linear control
I think you are asking the wrong question.

Is there really any point in doing this while operating in the linear region? From your question I'm guessing you want to control something like a DC motor, hence my answer will be directed at that.

A more appropriate way to control a DC motor, specially if you are using an arduino (which I assume you are since you used the arduino tag), is to simply use a full H bridge driven by PWM signals. A popular IC for small DC motors is the L293D - which is basically just 4 half-bridges.

Since you want bidirectional control, you can simply use a H bridge with PWM control. There exists unipolar PWM and bipolar PWM control. As an example, I will be explaining bipolar control since it's easier to understand: you apply PWM control to your entire H bridge, such that logic High in one arm turns one transistor on and the other off, and you make sure that the opposite happens in the other arm, like so:



With a 50% duty cycle, your motor turns slightly to one side, and then slightly to another. Do this fast enough and it doesn't even move. From 0%-50% it turns in one direction, while from 50%-100% it turns in the other.

Ok, but what if you actually want a sinusoidal output waveform and you are not controlling a DC motor? In that case you have a few different options. One of them is to use a DAC to generate your sine waveform, and then buffer that signal using an opamp in a voltage buffer/unit-gain configuration. This will be enough to power very light loads. A better option is to just simply use a buck converter topology, where you just switch a MOSFET using a PWM modulated sine wave, and let an LC filter take of eliminating the high-frequency harmonics for you. You might also want to add a series capacitor to the output to obtain a truly AC waveform.