  This paper is devoted to discuss the stabilizability of a class of $ 2
\times2 $ non-homogeneous hyperbolic systems. Motivated by the example in
\cite[Page 197]{CB2016}, we analyze the influence of the interval length $L$ on
stabilizability of the system. By spectral analysis, we prove that either the
system is stabilizable for all $L>0$ or it possesses the dichotomy property:
there exists a critical length $L_c>0$ such that the system is stabilizable for
$L\in (0,L_c)$ but unstabilizable for $L\in [L_c,+\infty)$. In addition, for
$L\in [L_c,+\infty)$, we obtain that the system can reach equilibrium state in
finite time by backstepping control combined with observer. Finally, we also
provide some numerical simulations to confirm our developed analytical
criteria.
