Fix CI: correct H∞ bound in the reduction tests and de-flake the scaling-invariance tests

[baggepinnen]

CI on master is red on a single assertion in test/test_reduction.jl:

Expression: norm(sysi * (sys - sysr), Inf) < 0.4
 Evaluated: 0.45825876482743627 < 0.4

The bad bound

This is not a regression in this package — #153 only touched Project.toml. It is a dependency bump: the last passing run resolved ControlSystemsBase v1.20.4, the failing one resolved v1.21.0, which reworked _infnorm_two_steps_ct, the kernel behind hinfnorm / norm(·, Inf).

The test system is hardcoded, so the failure is fully deterministic. Pinning ControlSystemsBase back to 1.20.4 in an otherwise identical environment restores the old value:

ControlSystemsBase	norm(G, Inf)	reported ω
1.20.4	0.31417	Inf
1.21.0	0.45826	139.44

The brute-force peak gain of G = sysi*(sys - sysr) over a 200k-point grid from 1e-4 to 1e4 rad/s is 0.458258, and hinfnorm2 (via DescriptorSystems, unchanged across the bump) gives 0.458196 on both versions. So 1.21.0 is right and the old value was a bad under-estimate: G has a state dimension of 23 with near-cancelled poles from fudge_inv sitting close to the imaginary axis, and on that system the old algorithm got stuck at the lower bound opnorm(D) — hence the reported ω = Inf.

The bound of 0.4 was therefore calibrated against a wrong number rather than against the true norm, and is raised to 0.5. The reduction itself is unchanged across the bump: norm(sys-sysr, Inf), the DC-gain residual property and the comparison against baltrunc all give identical values on both versions.

The flaky scaling-invariance tests

Separately, the three scaling-invariance tests compared hinfnorm2(minreal(sys1 - sys2))[1] against an absolute tolerance. sys_siso = ssrand(1,1,9,proper=true) is unseeded, and for roughly 5% of draws minreal leaves a near-cancelled pole close enough to the imaginary axis that ghinfnorm returns Inf and the test fails (2/50 and 2/30 in two measurement loops). This is unrelated to the ControlSystemsBase change — it happened to pass in the failing run — but it would have bitten eventually.

They now compare the frequency responses on a grid, which is what the section comments already claimed they did. Worst relative difference over 200 random draws:

check	worst over 200 draws
baltrunc2	5.0e-13
baltrunc_coprime	1.4e-11
baltrunc_unstab	5.0e-13

so the 1e-8 relative tolerance keeps a wide margin while being three orders of magnitude tighter than the old absolute 1e-5. sys_siso is left unseeded so the tests keep sampling new systems.

Verification

• A daemon session that deterministically reproduces the unlucky draw returning Inf now passes it, 3/3 runs.
• test_reduction.jl in 4 fresh processes: 45 passed, 4 broken, exit 0.
• Full suite against ControlSystemsBase 1.21.0: 1414 passed, 6 broken, 0 failed (the failing CI run had 1413 passed + 1 failed).

🤖 Generated with Claude Code

[codecov-commenter]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.90%. Comparing base (5fafc2e) to head (fa381b5).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #154   +/-   ##
=======================================
  Coverage   91.90%   91.90%           
=======================================
  Files          20       20           
  Lines        3065     3065           
=======================================
  Hits         2817     2817           
  Misses        248      248           

Flag	Coverage Δ
unittests	91.90% <ø> (ø)

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.