Almost ready to go, LQG remains

Author: mfalt

README.md

@@ -46,7 +46,7 @@ Some of the available commands are:
 ##### Constructing systems
 ss, tf, zpk, ss2tf
 ##### Analysis
-pole, tzero, sysnorm, norminf, ctrb, obsv, gangoffour, margin, markovparam, damp, dampreport, zpkdata, dcgain, covar, gram, sigma, sisomargin
+pole, tzero, norm, norminf, ctrb, obsv, gangoffour, margin, markovparam, damp, dampreport, zpkdata, dcgain, covar, gram, sigma, sisomargin
 ##### Synthesis
 care, dare, dlyap, lqr, dlqr, place, pid, leadlink, laglink, leadlinkat, rstd, rstc, dab
 ##### Time and Frequency response

REQUIRE

@@ -5,3 +5,4 @@ LaTeXStrings
 OrdinaryDiffEq
 IterTools
 Colors
+DSP

docs/src/lib/analysis.md

@@ -16,7 +16,7 @@ gangofseven
 gram
 margin
 markovparam
-sysnorm
+norm
 obsv
 pole
 sigma

src/ControlSystems.jl

@@ -80,6 +80,7 @@ import Base: +, -, *, /, (==), (!=), isapprox, convert, promote_op
 import LinearAlgebra: BlasFloat
 export lyap # Make sure LinearAlgebra.lyap is available
 import Printf, Colors
+import DSP: conv
 
 abstract type AbstractSystem end
 
@@ -129,8 +130,6 @@ include("plotting.jl")
 @deprecate num numvec
 @deprecate den denvec
 
-# @deprecate norm sysnorm
-
 # The path has to be evaluated upon initial import
 const __CONTROLSYSTEMS_SOURCE_DIR__ = dirname(Base.source_path())
 

src/analysis.jl

@@ -124,14 +124,14 @@ function tzero(A::Matrix{T}, B::Matrix{T}, C::Matrix{T}, D::Matrix{T}) where T<:
     mat = [C D]
     # To ensure type-stability, we have to annote the type here, as qrfact
     # returns many different types.
-    W = full(qrfact(mat')[:Q], thin=false)::Matrix{T}
-    W = flipdim(W,2)
+    W = qr(mat').Q
+    W = reverse(W, dims=2)
     mat = mat*W
     if fastrank(mat', meps) > 0
         nf = size(A, 1)
         m = size(D, 2)
         Af = ([A B] * W)[1:nf, 1:nf]
-        Bf = ([I zeros(nf, m)] * W)[1:nf, 1:nf]
+        Bf = ([Matrix{T}(I, nf, nf) zeros(nf, m)] * W)[1:nf, 1:nf]
         zs = eigvals(Af, Bf)
         _fix_conjugate_pairs!(zs) # Generalized eigvals does not return exact conj. pairs
     else
@@ -180,10 +180,10 @@ function reduce_sys(A::AbstractMatrix{T}, B::AbstractMatrix{T}, C::AbstractMatri
         end
         # Update System
         n, m = size(B)
-        Vm = [V zeros(T, n, m); zeros(T, m, n) I]
+        Vm = [V zeros(T, n, m); zeros(T, m, n) Matrix{T}(I, m, m)]
         if sigma > 0
             M = [A B; Cbar Dbar]
-            Vs = [V' zeros(T, n, sigma) ; zeros(T, sigma, n) I]
+            Vs = [V' zeros(T, n, sigma) ; zeros(T, sigma, n) Matrix{T}(I, sigma, sigma)]
         else
             M = [A B]
             Vs = V'

src/matrix_comps.jl

@@ -432,7 +432,12 @@ Glad, Ljung, Reglerteori: Flervariabla och Olinjära metoder
 function balreal(sys::StateSpace)
 P = gram(sys, :c)
 Q = gram(sys, :o)
-Q1 = cholesky(Q).U
+
+Q1 = try
+    cholesky(Q).U
+catch
+    throw(ArgumentError("Balanced realization failed: Observability grammian not positive definite, system needs to be observable"))
+end
 U,Σ,V = svd(Q1*P*Q1')
 Σ .= sqrt.(Σ)
 Σ1 = diagm(0 => sqrt.(Σ))

src/simplification.jl

@@ -11,7 +11,7 @@ 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::VecOrMat, B::VecOrMat, C::VecOrMat)
+function struct_ctrb_obsv(A::AbstractVecOrMat, B::AbstractVecOrMat, C::AbstractVecOrMat)
     costates = struct_ctrb_states(A, B) .& struct_ctrb_states(A', C')
     if !all(costates)
         inds = findall(costates)
@@ -23,11 +23,11 @@ end
 
 # Compute a bit-vector, expressing whether a state of the pair (A, B) is
 # structurally controllable.
-function struct_ctrb_states(A::VecOrMat, B::VecOrMat)
+function struct_ctrb_states(A::AbstractVecOrMat, B::AbstractVecOrMat)
     bitA = A .!= 0
-    d_cvec = cvec = any(B .!= 0, 2)
+    d_cvec = cvec = vec(any(B .!= 0, dims=2))
     while any(d_cvec .!= 0)
-        Adcvec = any(bitA[:, findall(d_cvec)], 2)
+        Adcvec = vec(any(bitA[:, findall(d_cvec)], dims=2))
         cvec = cvec .| Adcvec
         d_cvec = Adcvec .& .~cvec
     end

src/synthesis.jl

@@ -192,7 +192,7 @@ If no second system is given, negative identity feedback is assumed
 """
 function feedback(sys::StateSpace)
     sys.ny != sys.nu && error("Use feedback(sys1::StateSpace,sys2::StateSpace) if sys.ny != sys.nu")
-    feedback(sys,ss(Matrix{numeric_type(sys)}(I,ny,ny)))
+    feedback(sys,ss(Matrix{numeric_type(sys)}(I,sys.ny,sys.ny)))
 end
 
 function feedback(sys1::StateSpace,sys2::StateSpace)

src/timeresp.jl

@@ -247,6 +247,6 @@ _issmooth(u::Function) = false
 function _issmooth(u, thresh::AbstractFloat=0.75)
     u = [zeros(1, size(u, 2)); u]       # Start from 0 signal always
     dist = maximum(u) - minimum(u)
-    du = abs.(diff(u))
+    du = abs.(diff(u, dims=1))
     return !isempty(du) && all(maximum(du) <= thresh*dist)
 end

src/types/SisoTfTypes/SisoRational.jl

@@ -35,8 +35,8 @@ Base.zero(f::SisoRational) = zero(typeof(f))
 
 isproper(f::SisoRational) = (length(f.num) <= length(f.den))
 
-function minreal(sys::SisoRational, eps::Real=sqrt(eps()))
-    return SisoRational(minreal(SisoZpk(sys), eps))
+function minreal(sys::SisoRational{T}, eps::Real=sqrt(eps())) where T
+    return convert(SisoRational{T}, minreal(convert(SisoZpk,sys), eps))
 end
 
 function print_siso(io::IO, f::SisoRational, var=:s)