# # Five dim sys

# ## Model

module five_dim_sys #jl

using ReachabilityAnalysis

## system matrix
D = [-1.0 -4.0  0.0  0.0  0.0;
      4.0 -1.0  0.0  0.0  0.0;
      0.0  0.0 -3.0  1.0  0.0;
      0.0  0.0 -1.0 -3.0  0.0;
      0.0  0.0  0.0  0.0 -2.0]
P = [ 0.6 -0.1  0.1  0.7 -0.2;
     -0.5  0.7 -0.1 -0.8  0.0;
      0.9 -0.5  0.3 -0.6  0.1;
      0.5 -0.7  0.5  0.6  0.3;
      0.8  0.7  0.6 -0.3  0.2]
A = P * D * inv(P)

## state domain
X = Universe(5)

## input domain
U = Ball2(zeros(5), 0.01)

function model(X0)
    S = @system(x' = Ax + u, x ∈ X, u ∈ U)
    return IVP(S, X0)
end

end #jl

# ## References
