allow complex statespace matrices

[bnavigator]

Outsourced from #438, because it is not directly related to the test suite.

To be combined with #376

[coveralls]

Coverage increased (+0.005%) to 86.624% when pulling 0fda8c0 on bnavigator:complex-statespace into 51c797e on python-control:master.

[roryyorke]

I suspect this might be quite a lot of work to properly support (see below).

Would we change Slycot to reject complex matrices when real are expected? This might be a good idea anyway.

Would we support TFs with complex coefficients?

In [15]: import control as ct

In [16]: import control.matlab as ml

In [17]: ct.gram(ct.ss(-1-1j, 2, 3, 4), 'o')
/home/rory/.miniconda3/envs/controldev/lib/python3.8/site-packages/slycot/synthesis.py:792: ComplexWarning: Casting complex values to real discards the imaginary part
  out = _wrapper.sb03md(dico,n,C,A,U,job=job,fact=fact,trana=trana,ldwork=ldwork)
Out[17]: matrix([[4.5]])

In [18]: y, t = ml.step(ct.ss(-1-1j, 2, 3, 4)); y[1]
/home/rory/src/python-control/control/timeresp.py:376: ComplexWarning: Casting complex values to real discards the imaginary part
  xout[:, i] = (dot(Ad, xout[:, i-1]) + dot(Bd0, U[:, i-1]) +
Out[18]: 4.26995014112991

[bnavigator]

ComplexWarning: Casting complex values to real discards the imaginary part

Also, see discussion in #376. We could set a warning filter making this an error in Slycot.

[LSchmerber]

Hi,
First, thanks for this library.
I still have the complex values to float issue when starting matrix creation from complex eigen values and with Rev 0.9.0

[rico500]

Has the development for this feature been discontinued? Is there a big road-block depending on another package (slycot?)?

[lytex]

If I remember correctly, Slycot had some functions that could be easily extended to handle complex cases
#376 (comment)
However,

tb05ad_ng and tb04ad_r are casting complex values to real, but as far as I know it seems there are no complex routine equivalents to these functions

[bnavigator]

The main roadblock is probably developer time. I might resuming working on this not earlier than in 2 or 3 months. Contributions from others are always welcome of course.