Small delay with step errors

[albheim]

Was notified that running step on a system with a small delay creates some problem with dt <= dtmin from DifferentialEquations.jl which generates a warning and it seems like it does not create the saved values which errors when we try to index into them.

julia> step(delay(0.01))
t = 0.0:0.07:14.000000000000002
┌ Warning: dt <= dtmin. Aborting. There is either an error in your model specification or the true solution is unstable.
└ @ SciMLBase ~/.julia/packages/SciMLBase/EFFG1/src/integrator_interface.jl:345
ERROR: BoundsError: attempt to access 4-element Vector{Tuple{Vector{Float64}, Vector{Float64}}} at index [5]
Stacktrace:
 [1] getindex
   @ ./array.jl:801 [inlined]
 [2] _lsim(sys::DelayLtiSystem{Float64, Float64}, u!::Any, t::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}, x0::Vector{Float64}, alg::DelayDiffEq.MethodOfSteps{OrdinaryDiffEq.Tsit5, DiffEqBase.NLFunctional{Rational{Int64}, Rational{Int64}}, false}; kwargs::Base.Iterators.Pairs{Symbol, Float64, Tuple{Symbol, Symbol}, NamedTuple{(:abstol, :reltol), Tuple{Float64, Float64}}})
   @ ControlSystems ~/.julia/dev/ControlSystems/src/delay_systems.jl:204
 [3] lsim(sys::DelayLtiSystem{Float64, Float64}, u::ControlSystems.var"#299#300", t::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}; x0::Vector{Float64}, alg::DelayDiffEq.MethodOfSteps{OrdinaryDiffEq.Tsit5, DiffEqBase.NLFunctional{Rational{Int64}, Rational{Int64}}, false}, abstol::Float64, reltol::Float64, kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ ControlSystems ~/.julia/dev/ControlSystems/src/delay_systems.jl:99
 [4] step(sys::DelayLtiSystem{Float64, Float64}, t::StepRangeLen{Float64, Base.TwicePrecision{Float64}, Base.TwicePrecision{Float64}}; kwargs::Base.Iterators.Pairs{Union{}, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
   @ ControlSystems ~/.julia/dev/ControlSystems/src/delay_systems.jl:246
 [5] step
   @ ~/.julia/dev/ControlSystems/src/delay_systems.jl:238 [inlined]
 [6] #step#164
   @ ~/.julia/dev/ControlSystems/src/timeresp.jl:33 [inlined]
 [7] step(sys::DelayLtiSystem{Float64, Float64})
   @ ControlSystems ~/.julia/dev/ControlSystems/src/timeresp.jl:33
 [8] top-level scope
   @ REPL[21]:1

Here is a stripped down version of the code causing this problem, not sure if this is something that should be reported to DifferentialEquations or if we should work around it on our side.

using DelayDiffEq, DifferentialEquations
using ControlSystems
using LinearAlgebra

function f(du, u, h, p, t)
    tau = p
    # This is system for delay(tau) using two states based on our partitioned state space
    # y(t) = d(t-tau)
    # d(t) = u(t)
    hout = h(p, t-tau, Val{1}, idxs=2)
    du .+= [hout; 1]
end

t = 0:0.01:10
x0 = [0.0, 0.0]
p = 0.01

h!(p, t, deriv::Type{Val{1}}; idxs=0) = 0

prob = DDEProblem{true}(f, x0, h!,
            (t[1], t[end]),
            p,
            constant_lags=p,# Not sure if sort needed
            neutral=true,           # We have derivatives on RHS (d(t)) 
            )

sol = solve(prob, Tsit5(); tstops=t, saveat=t)