The "dead zone" is the frictional loss, its a torque, not a voltage, and its sign depends on the sign of omega, so you'd split the equation into two versions depending on the sign of omega. Solid friction is fairly close to being constant (independent of speed), but this is
only a first-order approximation.
V = k * omega + R/k (tau + 0.1), omega > 0
= k * omega + R/k (tau - 0.1), omega < 0
(although I might have gotten my sings wrong!)
All units are S.I., for instance k is Vs/rad or Nm/A (which are the same thing !)
Note that R increases somewhat as the motor heats up, though you can simplify things
if you assume its constant. Friction (the 0.1Nm) also changes as the motor heats up,
usually falling considerably, and then there's viscous friction to consider (air drag and
bearing friction) which can be dominant at top speed.