I have an underactuated mechanical system (linear bicycle model of a vehicle). I have two outputs that have to be controlled to zero and one input (you guessed it - steer angle, $\delta$). I have three exogeneous inputs, represented by $d_i$s. Following is the general structure of the state space for the error dynamics
$\begin{pmatrix} \dot{e}_1 \\ \dot{e}_2 \\ \dot{e}_3 \\ \dot{e}_4 \\ \end{pmatrix} = \begin{pmatrix} 0 & 1 & 0 & 0 \\ 0 & p_1 & p_2 & p_3 \\ 0 & 0 & 0 & 1 \\ 0 & p_4 & p_5 & p_6 \\ \end{pmatrix} \begin{pmatrix} e_1 \\ e_2 \\ e_3 \\ e_4 \\ \end{pmatrix} + \begin{pmatrix} 0 \\ b_1 \\ 0 \\ b_2 \\ \end{pmatrix} \delta + \begin{pmatrix} 0 & 0 & 0 \\ q_1 & q_2 & q_3 \\ 0 & 0 & 0 \\ 0 & q_4 & q_5 \\ \end{pmatrix} \begin{pmatrix} d_1 \\ d_2 \\ d_3 \\ \end{pmatrix}$
As can be seen, for feedforward control design, I have two error dynamics, $\dot{e}_2$ and $\dot{e}_4$, that need to go to $0$ asymptotically. But with one input, $\delta$, I can only choose it such that one of them can be tackled. What I mean is
$\delta = \delta_{fb} + \delta_{ff}$
I can choose $(\delta_{ff} = - q_1 \cdot d_1 - q_2 \cdot d_2 - q_3 \cdot d_3)$ or $(\delta_{ff} = - q_4 \cdot d_2 - q_5 \cdot d_3)$. i.e. to say I cannot select $\delta$ to satisfy both requirements. This is to say the system is underactuated. How can we deal with such a requirement?
Any reference source would be appreciated!