Fix struct_ctrb_obsv (#540)

* Fix struct_ctrb_obsv, closes #409

* Update src/simplification.jl

Co-authored-by: Fredrik Bagge Carlson <baggepinnen@gmail.com>

* add to docstring

Co-authored-by: olof3 <olof3@users.noreply.github.com>

src/simplification.jl

@@ -4,14 +4,24 @@
 Compute the structurally minimal realization of the state-space system `sys`. A
 structurally minimal realization is one where only states that can be
 determined to be uncontrollable and unobservable based on the location of 0s in
-`sys` are removed."""
+`sys` are removed.
+
+Systems with numerical noise in the coefficients, e.g., noise on the order of `eps` require truncation to zero to be
+affected by structural simplification, e.g.,
+```julia
+trunc_zero!(A) = A[abs.(A) .< 10eps(maximum(abs, A))] .= 0
+trunc_zero!(sys.A); trunc_zero!(sys.B); trunc_zero!(sys.C)
+sminreal(sys)
+```
+"""
 function sminreal(sys::StateSpace)
     A, B, C, inds = struct_ctrb_obsv(sys)
     return StateSpace(A, B, C, sys.D, sys.timeevol)
 end
 
 # Determine the structurally controllable and observable realization for the system
 struct_ctrb_obsv(sys::StateSpace) = struct_ctrb_obsv(sys.A, sys.B, sys.C)
+
 function struct_ctrb_obsv(A::AbstractVecOrMat, B::AbstractVecOrMat, C::AbstractVecOrMat)
     costates = struct_ctrb_states(A, B) .& struct_ctrb_states(A', C')
     if !all(costates)
@@ -22,15 +32,17 @@ function struct_ctrb_obsv(A::AbstractVecOrMat, B::AbstractVecOrMat, C::AbstractV
     end
 end
 
-# Compute a bit-vector, expressing whether a state of the pair (A, B) is
-# structurally controllable.
+"""
+    struct_ctrb_states(A::AbstractVecOrMat, B::AbstractVecOrMat)
+
+Compute a bit-vector, expressing whether a state of the pair (A, B) is
+structurally controllable based on the location of zeros in the matrices. 
+"""
 function struct_ctrb_states(A::AbstractVecOrMat, B::AbstractVecOrMat)
     bitA = A .!= 0
-    d_cvec = cvec = vec(any(B .!= 0, dims=2))
-    while any(d_cvec .!= 0)
-        Adcvec = vec(any(bitA[:, findall(d_cvec)], dims=2))
-        cvec = cvec .| Adcvec
-        d_cvec = Adcvec .& .~cvec
+    x = vec(any(B .!= 0, dims=2)) # index vector indicating states that have been affected by input
+    for i = 1:size(A, 1) # apply A nx times, similar to controllability matrix
+        x = (bitA * x) .!= 0
     end
-    return cvec
+    x
 end

test/test_simplification.jl

@@ -8,6 +8,9 @@ G = ss([-5 0 0 0; 0 -1 -2.5 0; 0 4 0 0; 0 0 0 -6], [2 0; 0 1; 0 0; 0 2],
 @test sminreal(G[2, 1]) == ss([-5], [2], [-2], [1])
 @test sminreal(G[2, 2]) == ss([-6], [2], [1], [0])
 
+using ControlSystems.DemoSystems: resonant
+R = resonant()*resonant()
+@test sminreal(R) == R # https://github.com/JuliaControl/ControlSystems.jl/issues/409
 
 ## MINREAL ##