# Can a system with a response Y(x) = ax + c be called linear?

I made a DC-DC converter its ideal transfer function is: $$V_0(D) = DV_i$$

I took measurements of its response and then made a linear regression, I got this result:

$$V_0(D) = 0.98DV_i -0.42$$

Quite similar to the expected value. Now, can I say that the system has a linear response?

strictly speaking, the system response should be zero when the input is zero, but in this case, if D = 0:

$$V_0 = -0.42$$

What would be the correct way to refer at the response of this system?

Edit:

Here is a plot of the theoric response, red, vs experimental values green. The 0.42 basically represents an offset because the losses of the system.

• I believe the term is affine – Nayuki Jun 5 '16 at 1:36
• Well it seems you have an awful small amount of data (only 8 points). It's hard to come to a conclusion about your system's response with so few observation points. – Lucas Franceschi Jun 5 '16 at 1:48
• I would say, it is linear in static states, but the behavior might be non-linear under dynamic conditions. – MaestroGlanz Jun 6 '16 at 8:11
• See also this question in relation to Nayuki's comment. – Karlo Jun 8 '16 at 15:47
• Probably your system have a bias. The switching maybe... – leCrazyEngineer Jul 17 '16 at 1:22

Well, I wouldn't say the result is quite similar, I don't have any information on scale or units of measurement but the $-0.42$ value might be significant. You should analyze other data, such as the correlation factor, and decide if the linear model you use to regress the data is appropriate.
EDIT: By the way, if a system does have a $Y(x) = ax + c$ response it is by definition linear, I think your question is whether your system does have such a response.