coverage: 94.607% (-0.02%) from 94.628% when pulling 55e2b55 on murrayrm:multivariable_interconnect-30Mar2023 into d834f7a on python-control:main.

Nice PR for this functionality. A few thoughts/comments:

1. What is the rationale for requiring lists rather than tuples to send sequences of signal names? Is it that tuples in this context are interpreted differently? Not possible to just call list() on the input arguments? (one less bug to get stuck on?)
2. Relatedly, when specifying signal ranges not as a slice, does this support the a somewhat hidden feature of numpy that indexing by tuples means something different than indexing by lists? Tuples are interpreted as coordinates into the array whereas lists are interpreted as selecting elements of the array. For example:

a = np.array((1,2,3))
a[0] // gives 1
a[(0,1]) // tuple indexing gives IndexError: too many indices for array: array is 1-dimensional, but 2 were indexed
a[[0,1]) // list indexing gives array([1, 2])

This could be used to access a subset of signals in a given name: sys.sig[[list_of_indices]]

3. Does this work for name-based auto-connection, that is, no connections keyword, provided all signals of the same name have the same size?

1. What is the rationale for requiring lists rather than tuples to send sequences of signal names? Is it that tuples in this context are interpreted differently? Not possible to just call list() on the input arguments? (one less bug to get stuck on?)

The problem is that with the new "abbreviated" ways of specifying signals, there can be ambiguity if you use a list instead of a tuple. For example, if we allowed tuples and lists to be used interchangeably, the output specification

outlist = ('P', 'z')

becomes ambiguous. Is this a single output with system 'P' and signal 'z' or did you mean the outputs of the system 'P' and also the signals 'z'? In this PR, this specification gets interpreted as the former case, whereas if you want the latter you would write

outlist=['P', 'z']

Note that here we have used the shorthand that you can specify the outputs of a block just by giving the name of the block ('P') and you can specify any output signal in the diagram (regardless of what subsystem it belongs to) just be specifying the signal name ('z'). (It is also possible that you mean signals 'P' and systems 'z', of course, and if there is ambiguity based on the specific subsystems then you get an error.)

2. Relatedly, when specifying signal ranges not as a slice, does this support the a somewhat hidden feature of numpy that indexing by tuples means something different than indexing by lists? Tuples are interpreted as coordinates into the array whereas lists are interpreted as selecting elements of the array. ....

This could be used to access a subset of signals in a given name: sys.sig[[list_of_indices]]

The only thing supported in this PR is ranges with optional upper and lower limits. If you want to index by a list, you would have to either list things out or use a list comprehension, such as [f'sys.sig[{i}]' for i in list_of_indices].

3. Does this work for name-based auto-connection, that is, no connections keyword, provided all signals of the same name have the same size?

That functionality was there before, since if you had a system with outputs [xd[0], xd[1], ..., xd[n]] and another system with those same signal names as inputs, then they would all connect together by virtue of matching in their enumerated form.

What you can do now that you couldn't do before is connect all of the xd's to new signals zd's (say) by saying something like

connections=[['zd', 'xd']]

OK, this looks good. One other question: I recently noticed that there is a bug in the current code in which system names and labels are lost when indexing the system:

e_summer = ct.summing_junction(['r', '-y'], 'e')
print(e_summer.input_labels)
print(e_summer[0,0].input_labels) # loses name and labels
print(e_summer[0,0].output_labels) # loses name and labels

gives

['r', 'y']
['u[0]']
['y[0]']

Any chance this PR addresses that?

This PR doesn't address __getitem__ signal naming, but this is a good place to fix that up.

One question is how to handle system naming. When we take a subset of a set of inputs and outputs we probably don't want to use exactly the same system name. Normally, we set the name to something like sysname$linearized or sysname$sampled and allow you to override the name in the function call. We can't do easy renaming here (since you can't add keywords to something like sys[2, [1, 2]]), but we can change the name to something like sys$indexed or sys_[2, [1, 2]] (though the latter might confuse some of our default name parsing, since we assume that names of the form "[\d]" are default system names).

sys$indexed seems reasonable to me - keeps the original name but provides indication that it is not the original system.

LGTM