I'm trying to find for this VARX*(2) $$x_t=a_0+a_1t+F_1x_{t-1}+F_2x_{t-2}+\Theta_0d_t+\Theta_1d_{t-1}+\Theta_2d_{t-2}+\varepsilon_t$$ an explicit form for $x_{T+n}$, i.e. solve it as an equation for the n-step ahead forecast. I know that for this VARX* $$x_t=a_0+a_1t+Fx_{t-1}+\Theta_0d_t+\Theta_1d_t+\varepsilon_t$$ the answer is $$x_{T+n}=F^nx_T+\sum_{\tau=0}^{n-1}F^{\tau}\big(a_0+a_1(T+n-\tau)\big)+\sum_{\tau=0}^{n-1}F^{\tau}(\Theta_0d_{T+n-\tau}+\Theta_1d_{T+n-\tau-1})+\sum_{\tau=0}^{n-1}F^{\tau}\varepsilon_{T+n-\tau}$$ but I do not fully understand how to use this answer to solve the VARX*(2) problem.
In the VARX*(1) case above, $x_{T+n}$ can be found from multiple left matrix multiplications but there is just one matrix $F$.
Is there a way to find that closed-form expression for the VARX*(2) n-step ahead forecast?