Which is the correct transfer function notation?

I noticed in the documentation for tf() and rlocus() that there are differing conventions on expressing numerators in the transfer function.

This example in tf() shows nonzeros for the coefficients going to the constant.

Whereas in rlocus() there is an example of this not being the case (in the numerator)

I was hoping to get some clarification so that I could accurately input the numerator and denominator into a transfer function. My understanding of these is not that great, so I apologize if there was an obvious answer I am missing.

Answer 1

[Paul]

Good catch. The documentation is incorrect. Assuming that sys represents the desired system, it should be entered as

sys = tf([0.5 0 -1],[4 0 3 0 2])

sys =
 
     0.5 s^2 - 1
  -----------------
  4 s^4 + 3 s^2 + 2
 
Continuous-time transfer function.

Also, another example on that doc page for "Closed-Loop Poles and Feedback Gain Values using Root Locus" has the same problem.