In this paper, systems described by state-space models are considered. For these systems, author studies the decoupling of linear systems and gives a sufficient condition for a system to be made feedback decouplable. Especially, the condition is given by LMI(Linear Matrix Inequality) form. Based on this condition, it is guaranteed that the system decoupling problem is achieved and the $H_{infty}$ constraint is satisfied simultaneously. This result can be easily extended to the robust decoupling control system design problems.