I think you're saying that system is nonlinear because there's a t^2, but it's actually linear. The ODE for the system is certainly linear. You could choose a s

I think you're saying that system is nonlinear because there's a t^2, but it's actually linear. The ODE for the system is certainly linear. You could choose a state space and describe the dynamics with linear operators. Solutions to linear ODEs are in general exponential or polynomial in time. The solution doesn't have to be linear for the system to be linear. (Unless I've misunderstood and you are modeling the system as actually controlling time. But I doubt that's what you meant)