use type parameter for E matrix

[baggepinnen]

If the field E is not associated with a type parameter, each access of E is type unstable, leading to a lot of inference problems and long compile times. This change brings a simple benchmark I have (using RobustAndOptimalControl which calls ghinfnorm in this package`) from

julia> using RobustAndOptimalControl, ControlSystems

julia> G = ssrand(2,2,2);

julia> @time hinfnorm2(G);
 18.141708 seconds (50.01 M allocations: 2.384 GiB, 8.45% gc time, 99.97% compilation time)

to

julia> @time hinfnorm2(G);
  6.451567 seconds (26.34 M allocations: 1.337 GiB, 7.95% gc time, 99.99% compilation time)

This is a step towards addressing the latest findings from

• Extreme compile times for some functions #9

[baggepinnen]

@andreasvarga CI will not automatically run on this PR since I'm a first-time contributor, there should be a button saying "approve" or something like that to press if you want to let CI run

[baggepinnen]

While running the tests locally, I get failures for methods with signatures like

Base.hcat(systems::DST...) where DST <: DescriptorStateSpace

since it requires all systems to be of exactly the same type, and thus fails when trying to concatenate

DescriptorSystems.DescriptorStateSpace{Int64, LinearAlgebra.UniformScaling{Bool}}, ::DescriptorSystems.DescriptorStateSpace{Int64, Matrix{Int64}}

where one E::UniformScaling and the other E::Matrix. I'm not sure how you want to handle this, perhaps making the signatures less strict like this?

Base.hcat(systems::DescriptorStateSpace...)

[andreasvarga]

This seems to be an useful feature. Have you tried jointly with
Base.hcat(systems::DescriptorStateSpace...) ?

[baggepinnen]

I haven't tried the suggested change, there were a lot of places that needed similar updates so I wanted to discuss the strategy before proceeding. I'll have a go at the suggested strategy tomorrow

[baggepinnen]

With the latest commit, tests pass locally, and this simple compile-time benchmark goes from

julia> using DescriptorSystems;

julia> G = rss(2,2,4);

julia> @time ghinfnorm(G);
 20.182468 seconds (59.23 M allocations: 2.710 GiB, 5.65% gc time, 100.00% compilation time)

to

julia> @time ghinfnorm(G);
  6.971881 seconds (24.47 M allocations: 1.197 GiB, 10.94% gc time, 99.99% compilation time)

To verify that we didn't get any run-time regressions, here's a benchmark of the runtime as well
Before:

julia> using BenchmarkTools

julia> @btime ghinfnorm($G);
  1.535 μs (23 allocations: 2.11 KiB)

After:

julia> @btime ghinfnorm($G);
  1.419 μs (23 allocations: 2.20 KiB)

All tests were performed on julia Version 1.8.0-beta1

[codecov]

Codecov Report

Merging #12 (1ea54fd) into main (9ab2700) will decrease coverage by 0.00%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main      #12      +/-   ##
==========================================
- Coverage   97.02%   97.01%   -0.01%     
==========================================
  Files          17       17              
  Lines        3457     3455       -2     
==========================================
- Hits         3354     3352       -2     
  Misses        103      103              

Impacted Files	Coverage Δ
src/connections.jl	94.78% <100.00%> (-0.05%)	⬇️
src/types/DescriptorStateSpace.jl	95.34% <100.00%> (ø)

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