Problem using inputs in `structural_simplify`

[dannys4]

using ModelingToolkit
N = 5
@variables t x_a[1:N](t) u_a[1:N](t) [input=true] y_a[1:N](t) [output=true]
D = Differential(t)
x, u, y = collect.([x_a, u_a, y_a])
A = rand(N,N); B = rand(N,N); C = rand(N,N);
eqs = [D.(x) .~ A*x + B*u; y .~ C*x]
sys = ODESystem(eqs, name=:linear_sys)
new_sys = structural_simplify(sys)

Error:

ERROR: ExtraVariablesSystemException: The system is unbalanced. There are 15 highest order derivative variables and 10 equations.
More variables than equations, here are the potential extra variable(s):
 x_a[1](t)
 x_a[2](t)
 x_a[3](t)
 x_a[4](t)
 x_a[5](t)
 u_a[1](t)
 u_a[2](t)
 u_a[3](t)
 u_a[4](t)
 u_a[5](t)

[ChrisRackauckas]

u is not marked as an input?

[dannys4]

See the newest revision-- I forgot to mark it as an input when I first posted 😅. It doesn't work without input=true, but that makes sense (if it's not an input state, not an output state, not a differentiated variable, and not a parameter, it's pretty unclear what it would be).

[YingboMa]

using ModelingToolkit
@variables t x_a[1:N](t) u_a[1:N](t) [input=true] y_a[1:N](t) [output=true]
@parameters fs[1:N](..)
D = Differential(t)
x, u, y, fs = collect.([x_a, u_a, y_a, fs])
A = rand(N,N); B = rand(N,N); C = rand(N,N);
eqs = [D.(x) .~ A*x + B*u; y .~ C*x; u .~ map(f->f(t), fs)]
sys = ODESystem(eqs, name=:linear_sys)
new_sys = structural_simplify(sys)