make feedback differentiable by avoiding try-catch

[baggepinnen]

Zygote.jl does not handle try-catch, so I modified feedback slightly to avoid using it, but maintained the useful error messagees.

The comment # inv seems to be better than lu made no sense to me since inv is literally implemented like this

Ai = inv!(lu(AA))

[JuliaControlBot]

Something failed when generating plots. See the log at https://github.com/JuliaControl/ControlExamplePlots.jl/actions/runs/1667112928?check_suite_focus=true for more details.

[codecov[bot]]

Codecov Report

Merging #596 (7cb95f6) into master (5c4a565) will increase coverage by 0.05%. The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #596      +/-   ##
==========================================
+ Coverage   86.64%   86.69%   +0.05%     
==========================================
  Files          31       31              
  Lines        3324     3322       -2     
==========================================
  Hits         2880     2880              
+ Misses        444      442       -2     

Impacted Files	Coverage Δ
src/connections.jl	93.90% <100.00%> (+1.13%)	:arrow_up:

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[baggepinnen]

Let's put his one on hold, Zygote doesn't actually support @warn either :/

[baggepinnen]

Note to self: hinfnorm fails with both ForwardDiff and ReverseDiff due to GLA's HessenbergFactorization having different fieldnames. ReverseDiff also falis to use the chain rule for hinfnorm due to the TrackedReal appearing in a field of an outer type. and thus RD is failing to pass "tracker free" variables into hinfnorm

typeof(sys) = ControlSystems.StateSpace{Continuous, ReverseDiff.TrackedReal{Float64, Float64, Nothing}}
ERROR: LoadError: type HessenbergFactorization has no field H

typeof(sys) = ControlSystems.StateSpace{Continuous, ForwardDiff.Dual{ForwardDiff.Tag{typeof(cost), Float64}, Float64, 4}}
ERROR: LoadError: type HessenbergFactorization has no field H