Controller for a direct-injection internal combustion engine and method of controlling the direct-injection internal combustion engine

A controller for a direct-injection internal combustion engine in which fuel is directly injected into a combustion chamber via a fuel injection valve, and a mixture formed thereby is burned by igniting the mixture via an ignition plug, wherein when the internal combustion engine is started under very low temperature conditions, the controller controls an ignition cut operation that inhibits ignition and performs fuel injection only, the controller comprising:

• an engine-start control unit,
• wherein when the internal combustion engine is started under the very low temperature conditions after the ignition cut operation was performed, the engine-start control unit determines, based on (1) whether an elapsed time since a start of the internal combustion engine under the very low temperature conditions becomes equal to or longer than a predetermined period of time or (2) a total amount of intake air since a start of the internal combustion engine becomes equal to or greater than a predetermined amount, whether there is a cylinder-inside warming-up history, and, unless a predetermined cancellation condition is satisfied when there is the cylinder-inside warming-up history, the engine-start control unit inhibits the ignition cut, or limits a number of times the ignition cut operation is to be performed.