output extra information from linearization

[baggepinnen]

also change the use of the symbol u in docstrings and warning messages for the more explicit unknowns to not confuse users of input-output functions, where u is traditionally (also in our docs) used to denote input rather than state.

[AayushSabharwal]

If this is to aid in debugging initialization, then #3418 addresses exactly this issue, and would apply here as well.

[AayushSabharwal]

Isn't returning success unnecessary? If !success then we error, so at this point success is guaranteed to be true.

[ChrisRackauckas]

should this be a ReturnCode?

[baggepinnen]

If this is to aid in debugging initialization, then #3418 addresses exactly this issue, and would apply here as well.

The primary motivation for this is that a linearized model is representing the dynamical system

$$\begin{aligned} \Delta \dot x &= A\Delta x+B\Delta u \\\ y &= C\Delta x + D \Delta u \end{aligned}$$

where $\Delta x = x - x_{op}$, so knowing what $x_{op}$ resolves to is often of interest, and since this is computed anyways, we might as well return it