This error occurs with conda forge's slycot 0.2.0, 0.3.0, and 0.3.3.

How precise is this test? I can imagine minreal being finicky because of floating point operations. How robust is it to different platforms, architectures, and blas/lapack implementations?

Good to know that this is not a new bug. I was pretty sure I had seen the error message before, but couldn't figure out where.

I chased this down a bit. It looks like what is happening is that one of the (random) state space systems that is getting generated in the unit test has a near pole-zero cancellation. minreal() is not reducing the system (via a call to tb01pd ). But when the unit test checks to make sure minreal is not changing the system, it converts the state space system to a transfer function and one of systems is now reduced (inside of tb04ad, where it extracts the controllable-observable subsystem). This is probably just a difference in tolerances, as @moorepants indicated. Interestingly, the error doesn't show up on my local system if I use the lapack variant of slycot instead of the openblas variant.

Here are the systems that are being compared:

System 1 (original):

A = [[-2.07272289  0.16120168  0.05029039 -0.17656953]
 [-1.2172162  -3.0412386   0.87634026  0.45936988]
 [ 2.34727018  2.1024825  -2.97194391 -1.72217184]
 [ 2.70301798  2.1897608  -1.33329543 -3.77801591]]

B = [[ 0.22934264]
 [-1.05015731]
 [-0.40877983]
 [-1.282876  ]]

C = [[-1.22961654  0.9999803  -0.         -0.        ]]

D = [[0.]]

   -1.332 s^2 - 10.37 s - 13.7
---------------------------------
s^3 + 9.665 s^2 + 26.21 s + 21.53

Zeros =  [-6.09568359 -1.68756532]
Poles =  [-5.76863334 -2.1991448  -1.69699836]

System 2 (output of minreal):

A = [[-1.44793116  0.00720403 -1.02465799 -0.32451831]
 [ 1.29258628 -2.23726554 -1.36828447 -1.39979547]
 [ 2.18253992 -0.07706622 -4.41025255 -2.57508146]
 [ 1.75507481 -0.03186882 -2.0133189  -3.76847205]]

B = [[-1.09979463]
 [ 0.78245651]
 [-0.96370783]
 [-0.46667011]]

C = [[ 0.         -1.46759237 -0.09533846  0.59076278]]

D = [[0.]]

   -1.332 s^3 - 13.3 s^2 - 36.51 s - 30.14
---------------------------------------------
s^4 + 11.86 s^3 + 47.46 s^2 + 79.16 s + 47.34

Zeros =  [-6.09568359 -2.1991448  -1.68756532]
Poles =  [-5.76863334+0.00000000e+00j -2.1991448+2.29466803e-07j
 -2.1991448-2.29466803e-07j -1.69699836+0.00000000e+00j]

The cancellation is occurring in the first system but not the second. In particular, in the second system there is a zero at -2.1991448 and a pair of poles at -2.1991448 +/- 2.29466803e-07j (one of which gets apparently gets cancelled in the first system).

There are two issues here:

• The criterion in minreal for a pole/zero cancellation is different than in ss2tf.
• The minreal unit test is not testing (just) minreal, but is also (implicitly) testing th ss2tf conversion.

Not sure yet what the right fix is (if any).

Fixed in #220.