TLV171: TLV171 for floating ground circuit

The circuit's output is not floating. "Virtual ground" means that it is not the same as the ground that is labeled "GND".

The R5;R12 voltage divider generates 1/20th of the circuit's output voltage.

When the circuit's output voltage is the same as 20× the control voltage, then the opamp's two input voltages are the same.
When the circuit's output voltage happens to be larger than 20× the control voltage, then the voltage at the opamp's noninverting input is higher than that at its inverting input, and the opamp increases its output voltage. This increases the transistor's base current, and makes the transistor sink more current, thus reducing the circuit's output voltage.
When the circuit's output voltage happens to be smaller than 20× the control voltage, the same happens in inverse.

Hey Maggie, 

The circuit uses an integrator circuit, here is the design note: Integrator circuit

I ran a sim, please see attached here: 2018.Integrator.zip

You can see see what Clemens has explained above. 

Maggie Li said:

Customers are using TLV171 to provide a floating ground for LDO.

From my interpretation, this circuit does not provide a "floating ground," if there is a difference between grounds, it will detect and correct.