Simple analogue=>pwm circuit with inverting and noninverting outputs
Whole tribes are fighting religious wars over the microcontroller vs. 555 debate. I'm on the microcontroller side.  

So the first question is: does it have to be a 555, and what are the arguments for it? (that's two questions.) There may be good reasons for it, but I'd like to know them. "My wife wants me to do it this way" is not a good reason (unless maybe when I see her). Without a good reason I'd have a look at the microcontroller.

The main advantages of the microcontroller are simplicity and accuracy. Simplicity as in you only need a microcontroller and a potmeter to set the duty cycle. Two parts for the complete circuit, or one if your analog control voltage comes from elsewhere in the circuit; then you can drop the potmeter. Accuracy as in 10 bits ADC translates in 10 bit PWM, that's 0.1 % precision at a 1 % accurate clock. Make that a 20 ppm clock if you want to add a crystal. Accuracy is also reproducibility.  

OTOH the 555 can work at 15 V if necessary, which the microcontroller can't, and doesn't need programming. The latter is again one of those religious things, but in practice writing a program for this can be done as quickly as designing and calculating the 555 circuit: setup two identical PWM channels but one inverted, the other non-inverted, and in a loop read the ADC and copy the value to both PWM registers.
So the microcontroller outputs complementary signals without external components.

The 555 circuit relies on a capacitor and if you want that at 1 % tolerance you'll pay a few times more than what the microcontroller costs. And even then the frequency will vary with the duty cycle.  

All in all there are few 555 applications which a microcontroller can't do better.