Control unit for direct injection engine

When a direct injection type internal combustion engine is in an operating state, a fuel is split and jetted into a cylinder of the internal combustion engine and split injections are performed in a manner to make a ratio of a piston travel and an injection pulse width of split injection constant in a cycle whereby a rich mixture is not locally generated and a mixture in a cylinder of the internal combustion engine is put in a condition near stoichiometry. Also, when the internal combustion engine is in cold condition, a fuel is split and jetted and split injections are performed so that the ratio of the piston travel and the injection pulse width of split injections monotonously increases in a cycle.