numpy.ndarray * control.TransferFunction gives array object

TransferFunction doesn’t have the __array_priority = 11 class attribute that StateSpace and FrequencyResponseData do. Is this on purpose? See below for results of array * tf, which results in an array (dtype object), and array * ss, which results in a SS object. I found this while investigating the behaviour of bdalg.connect in relation with #421

Should multiplication of scalar transfer functions by arrays be special-cased so that, e.g., with scalar tf k, k * eye(5) gives a 5x5 TF with identical entries on the diagonal? I think this sort of convention is used in literature, but it might be tricky to get something consistent here (e.g., should 1-input 1-output state-space systems do something analogous?; should one do general broadcasting?)

(control-dev) rory@rory-latitude:~/src/python-control$ ipython
Python 3.8.5 | packaged by conda-forge | (default, Jul 31 2020, 02:39:48) 
Type 'copyright', 'credits' or 'license' for more information
IPython 7.17.0 -- An enhanced Interactive Python. Type '?' for help.

In [1]: !git describe                                                                                                  
0.8.3-62-g6ede92e

In [2]: import control                                                                                                 

In [3]: import numpy as np                                                                                             

In [4]: np.array([[1]]) * control.tf([1], [1,1])                                                                       
Out[4]: array([[TransferFunction(array([1.]), array([1, 1]))]], dtype=object)

In [5]: np.array([[1]]) * control.ss([[-1]], [[1]], [[1]], [[0]])                                                      
Out[5]: StateSpace(array([[-1.]]), array([[1.]]), array([[1.]]), array([[0.]]))

[murrayrm]

My two cents:

• As much as possible, it seems like all LTI objects should behave the same with respect to various operations. So it shouldn’t matter if you have a TransferFunction or a StateSpace system of an LTI system.

• It also seems to me that if a control system object (LTI or InputOutputSystem) is in an expression where you would expect to get back a control system object, things should work as expected. This basically prioritizes the control objects over numpy objects (I think).

For the specific case above, I would have expected to get a TransferFunction back. I’d be interested to hear what others things about this.

[murrayrm]

LinearIOSystem and InterconnectedSystems are both subclasses of InputOutputSystem. Any operation with an LTI system that can be converted to a StateSpace system can (and probably should) be promoted to an InputOutput system. Note that you can’t combine an FRD system with an InputOutputSystem since the former is has (only) a frequency domain representation and later has (only) a state space representation.