Hi richard,
I am not familiar with LQR controller, but I guess the following may be helpful.
What you're looking for is: 
i.e. Minimum inductor current needed to provide 
.
.You may get started from the following two parameters:
: output power rating of the boost converter
: steady state operating voltages at input and output
Using these, within the boundaries of certain assumptions, it's possible to get to the right answer.
In one switching cycle 
, the charge is transferred from input to output only when the switch is Open. i.e. 
, where d is the duty cycle of the PWM switching.
, the charge is transferred from input to output only when the switch is Open. i.e. , where d is the duty cycle of the PWM switching.
Using the above two, it is possible to establish a relationship between input and out voltages at steady state,
Using (1), you may also find rated / steadystate value of 
.
.But maybe that's something you're probably not interested at the moment. What you need is .
.This needs somewhat familiarity with converter design. It also depends on topology.
For simplicity, I'm assuming non-isolated boost converter operating in Continuous Conduction Mode (CCM).
The values for inductor & capacitor for such a coverter maybe computed by [1],
Where, 
is the Inductor current ripple & 
is the switching frequency.
is the Inductor current ripple & is the switching frequency.The boost converter will be in CCM (and hence start working) at 
.
.There lies your answer. Depending upon converter topology and control system, you'd have to derive new equations for arriving at above value.
Hope this helps. Have a good day.
[1] Singh B, Singh S. Single-phase power factor controller topologies for permanent magnet brushless DC motor drives. IET power electronics. 2010 Mar 1;3(2):147-75.
