Nonlinear system with input integral in the state

Question

I have a nonlinear system of the type:

\begin{equation} \dot{\omega} = A(\omega, u) + B(\omega, u)\cdot \dot{u} \end{equation}

That is, the state is a function of the integral of the input $\dot{u}$. How can I solve this numerically (e.g. ode45 in Matlab)? Should I create an augmented state of the type: \begin{equation} \begin{bmatrix} \dot{\omega}\\ \dot{u} \end{bmatrix}= f(w,u) \end{equation} I am a little confused..