The model structure of Iyama-Yoshino's subfactor triangulated categories

Let $\X$ be a homological finite subcategory of an additive category $\C$. Under suitable conditions, we prove that the stable category $\C/\X$ as the homotopy category of a closed model structure on $\C$ induced by $\X$ is a triangulated category. This shows that Iyama-Yoshino's subfactor triangulated categories have closed model structure.