add numerical challenge problem to tests

Author: baggepinnen

Project.toml

@@ -41,8 +41,8 @@ UnPack = "1.0"
 julia = "1.6"
 
 [extras]
-GenericLinearAlgebra = "14197337-ba66-59df-a3e3-ca00e7dcff7a"
 FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+GenericLinearAlgebra = "14197337-ba66-59df-a3e3-ca00e7dcff7a"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

src/hinfinity_design.jl

@@ -158,7 +158,7 @@ function hinfsynthesize(
         _γiterations(P̄, interval, verbose, gtol, tolerance)
 
 
-    if !isempty(γFeasible)
+    if γFeasible !== nothing
         # Synthesize the controller and transform it back into the original coordinates
 
         if γrel > 1
@@ -448,7 +448,7 @@ function _γiterations(
 
     T = typeof(P.A)
     XinfFeasible, YinfFeasible, FinfFeasible, HinfFeasible, gammFeasible =
-        T(undef,0,0), T(undef,0,0), T(undef,0,0), T(undef,0,0), typemax(interval[2])
+        T(undef,0,0), T(undef,0,0), T(undef,0,0), T(undef,0,0), nothing
 
     gl, gu = interval
     gl = max(1e-3, gl)

test/test_hinf_design.jl

@@ -851,3 +851,22 @@ end
     end
 end
 
+
+@testset "Numerical difficulties" begin
+    ## Numerically difficult problem instance
+    Gsyn3A = [0.0 1.0 0.0; -1.2000000000000002e-6 -0.12000999999999999 0.0; -11.2 -0.0 -2.0e-7]
+    Gsyn3B = [0.0 0.0; 0.0 1.0; 1.0 0.0]
+    Gsyn3C = [-7.466666666666666 -0.0 19.999999866666666; 0.0 0.0 0.0; -11.2 -0.0 0.0]
+    Gsyn3D = [0.6666666666666666 0.0; 0.0 1.0; 1.0 -0.0]
+    Gsyn3 = ss(Gsyn3A, Gsyn3B, Gsyn3C, Gsyn3D)
+    Gsyn = partition(Gsyn3, 1, 2)
+    K, γ = hinfsynthesize(Gsyn, ftype=BigFloat, γrel = 1)[1:2]
+    @test_broken γ ≈ 4.4825150 atol=1e-2 # value by slicot
+    @test γ ≈ 4.4825150 atol=2e-2 # slightly less strict test is passed
+
+
+    Gsynb, _ = balance_statespace(Gsyn, false)
+    K, γ = hinfsynthesize(Gsynb, ftype=BigFloat, γrel = 1)[1:2]
+    @test_broken γ ≈ 4.4825150 atol=1e-2 # value by slicot
+    @test γ ≈ 4.4825150 atol=2e-2 # slightly less strict test is passed
+end