I'm currently trying to implement an algorithm I found in a paper on occupancy detection. I have to "choose" values of $L_1$ and $L_2$ such that the matrix below would be a Hurwitz matrix.
Let $b_X \neq 0 $ and choose $L_1, L_2$ such that the matrix $$A - \begin{pmatrix} L_1 \\ L_2 \end{pmatrix}C$$ is Hurwitz, where
$$A = \begin{pmatrix} -a & 0 \\ 0 & 0 \end{pmatrix}, \qquad C = (\pi_1(1) \quad \pi_2(1))$$
I know what a Hurwitz matrix is. However, how would I go about selecting values of $L_1$ and $L_2$ to ensure $A-LC$ is Hurwitz?
$\pi_1(1)$ and $\pi_2(1)$ resolve to 0.6072564843117833 and -0.12096559347742719 respectively. $b_X = 1.5$ and $a = 1/16.67$
edit:
$\pi_1(1)$ and $\pi_2(1)$ are given by;
$\pi_1(x) = \frac{b_X}{a}(e^\frac{ax}{b}-1)$
$\pi_1(x) =\frac{b_X}{ba}x + \frac{b_X}{a^2}(1-e^\frac{ax}{b})$
where $b = 2.5$, $b_x = 1.5$, $1/a = 16.67$