I'm trying to solve an equation from the next form:
$$\begin{eqnarray*} x_1'(t)&=&x_2(t) \\ \\x_2'(t)&=&-0.25x_1(t)-u(t)x_2(t) \end{eqnarray*}$$
I'm not sure how to solve this because there is a multiple between the controller $u(t)$ and the state space $x_2(t)$.
My question is how can i proceed with solving this using Hamiltonian in this case.
Thank you.