Controller and control method for internal combustion engine

A controller configured to control an internal combustion engine that includes an exhaust purification device, which purifies exhaust gas discharged from a plurality of cylinders, fuel injection valves provided for the respective cylinders, and a multi-speed transmission coupled to a crankshaft, wherein

• the controller comprises processing circuitry
• the processing circuitry is configured to execute
• a dither control process of operating the fuel injection valves such that at least one of the cylinders is a lean combustion cylinder, in which an air-fuel ratio is leaner than a stoichiometric air-fuel ratio, and at least another one of the cylinders is a rich combustion cylinder, in which an air-fuel ratio is richer than the stoichiometric air-fuel ratio, and
• a limiting process of limiting the dither control process such that a difference in the air-fuel ratio between the cylinders is smaller in a change period, in which a gear ratio of the multi-speed transmission is changed, than in periods except for the change period.