Test of DADE

DADE.jl

using DelayDiffEq
using DifferentialEquations
using Plots
A = -1.0
B = 1.0
C = 0.5
D = 0.0

function f(du, u, h!, p, t)
    (A,B,C,D,tmp,Tau) = p
    h!(tmp, p, t-Tau[1]) # Get delayed signal
    du[1] =         A*u[1] + B*tmp[2] # x'(t) = A*x(t) + B*d(t-tau)
    du[2] = -u[2] + C*u[1] + D*tmp[2] # d(t)  = C*x(t) + D*d(t-tau)
end

f2 = DDEFunction(f, mass_matrix = [1.0 0; 0 0])

Tau = [1.0,]
tmp = fill(0.0, 2)
p = (A,B,C,D,tmp,Tau)
# Second state zero before time starts
x0 = [1.0, 0.0]
h!(out, p, t) = (out .= x0)

prob = DDEProblem{true}(f2, x0, h!, (0.0, 2), p, constant_lags=Tau)

sol = solve(prob, MethodOfSteps(Tsit5()))
plot(sol)

plot!(0:0.1:1, x->exp(-x), lab="Ref u1")
plot!(0:0.1:1, x->0.5*exp(-x), lab="Ref u2")