using ReachabilityAnalysis, SparseArrays
using ReachabilityModels: @relpath

system matrix

I = [1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 7, 8]
J = [2, 3, 2, 1, 2, 3, 4, 1, 6, 7, 6, 5, 6, 7, 8, 5]
V = [1, 8487.2, -1.0865, -2592.1, -21.119, -698.91, -141399.0, 1.0, 1.0,
     8487.2, -1.0865, -2592.1, -21.119, -698.91, -141399.0, 1.0]
A = sparse(I, J, V)
8×8 SparseArrays.SparseMatrixCSC{Float64, Int64} with 16 stored entries:
      ⋅     1.0         ⋅           ⋅        ⋅      ⋅          ⋅           ⋅ 
      ⋅    -1.0865  8487.2          ⋅        ⋅      ⋅          ⋅           ⋅ 
 -2592.1  -21.119   -698.91  -141399.0       ⋅      ⋅          ⋅           ⋅ 
     1.0     ⋅          ⋅           ⋅        ⋅      ⋅          ⋅           ⋅ 
      ⋅      ⋅          ⋅           ⋅        ⋅     1.0         ⋅           ⋅ 
      ⋅      ⋅          ⋅           ⋅        ⋅    -1.0865  8487.2          ⋅ 
      ⋅      ⋅          ⋅           ⋅   -2592.1  -21.119   -698.91  -141399.0
      ⋅      ⋅          ⋅           ⋅       1.0     ⋅          ⋅           ⋅ 

input matrix

B = sparse([4, 8], [1, 2], [-1.0, -1.0])
8×2 SparseArrays.SparseMatrixCSC{Float64, Int64} with 2 stored entries:
   ⋅     ⋅ 
   ⋅     ⋅ 
   ⋅     ⋅ 
 -1.0    ⋅ 
   ⋅     ⋅ 
   ⋅     ⋅ 
   ⋅     ⋅ 
   ⋅   -1.0

state domain

X = Universe(8)
Universe{Float64}(8)

input domain

U = Hyperrectangle([0.23, 0.3], [0.07, 0.1])

function model(X0)
    S = @system(x' = Ax + Bu, x ∈ X, u ∈ U)
    return IVP(S, X0)
end
model (generic function with 1 method)